title: Happiness

text: On the other hand, there have been many studies that have found genetics to be a key part in predicting and understanding happiness in humans. In a review article discussing many studies on genetics and happiness, they discussed the common findings. The author found an important factor that has affected scientist findings this being how happiness is measured. For example, in certain studies when subjective wellbeing is measured as a trait heredity is found to be higher, about 70 to 90 percent. In another study, 11,500 unrelated genotypes were studied, and the conclusion was the heritability was only 12 to 18 percent. Overall, this article found the common percent of heredity was about 20 to 50 percent.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is a coastal city on the east coast of the United States in Horry County, South Carolina. It is located in the center of a long and continuous stretch of beach known as "The Grand Strand" in northeastern South Carolina.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is one of the major centers of tourism in South Carolina and the United States. The city's warm subtropical climate, miles of beaches, 86 golf courses, and 1,800 restaurants attract over 20 million visitors each year, making Myrtle Beach one of the most visited destinations in the country.


title: Myrtle Beach, South Carolina

text: Located along the historic King's Highway (modern U.S. Route 17), the region was once home to the Waccamaw people. During the colonial period, the Whither family settled in the area, and a prominent local waterway, Wither's Swash, is named in their honor. Originally called alternately "New Town" or "Withers", the area was targeted for development as a resort community by Franklin Burroughs, whose sons completed a railroad to the beach and the first inn, Seaside Inn. His widow named the new community Myrtle Beach after the local wax-myrtle shrubs.


title: Myrtle Beach, South Carolina

text: The Myrtle Beach metropolitan area is the second-fastest-growing metropolitan area in the country with a population of 35,682 in the 2020 census and more than 104,000 people moved to the Myrtle Beach-Conway-North Myrtle Beach area over eight years, representing in a 27.7% growth in population according to the U.S. Census Bureau.


title: Myrtle Beach, South Carolina

text: Prior to the arrival of Europeans, the Long Bay area was inhabited by the historic Waccamaw tribe. The Waccamaw used the river for travel and fished along the shore around Little River. Waties Island, the primary barrier island along Long Bay, has evidence of burial and shell mounds, remains of the visiting Waccamaw.


title: Myrtle Beach, South Carolina

text: The first European settlers along Long Bay arrived in the late 18th century, attempting to extend the plantation system outward toward the ocean. Records are sparse from this period, with most of the recorded history pieced together from English colonial land grant documents. These settlers gained mixed results, producing unremarkable quantities of indigo and tobacco, the two major commodity crops. The coast's soil was sandy and most of the crop yields were of inferior quality.


title: Myrtle Beach, South Carolina

text: Prior to the American Revolution, the area along the future Grand Strand was essentially uninhabited. Several families received land grants along the coast, including the Witherses: John, Richard, William, and Mary. This family received an area around present-day Wither's Swash, also known as Myrtle Swash or the Eight-Mile Swash. A separate grant was granted to James Minor, including a barrier island named Minor Island, now Waties Island, off the coast near Little River.


title: Myrtle Beach, South Carolina

text: Mary Withers's gravestone at Prince George Winyah Parish Church speaks to the remoteness of the former Strand: "She gave up the pleasures of Society and retired to Long Bay, where she resided a great part of her life devoted to the welfare of her children."


title: Myrtle Beach, South Carolina

text: As the American colonies gained independence, the area remained essentially unchanged, and the coast remained barren. George Washington scouted out the Southern states during his term, traveling down the King's Highway. He stayed a night at Windy Hill (part of present-day North Myrtle Beach) and was led across Wither's Swash to Georgetown by Jeremiah Vereen.


title: Myrtle Beach, South Carolina

text: The Withers family remained one of the few settlers around Myrtle Beach for the next half-century. In 1822, a strong hurricane swept the house of R. F. Withers into the ocean, drowning 18 people inside. The tragedy made the Withers family decide to abandon their plots along the coast. Left unattended, the area began to return to forest.


title: Myrtle Beach, South Carolina

text: The Burroughs and Collins Company of Conway, predecessor of modern-day Burroughs & Chapin, purchased much of the Withers family's land in 1881. The growing community was called "New Town" around the start of the 20th century. A post office named "Withers" was established to serve the site of the old Swash in 1888. On 28 February 1899, Burroughs and Collins received a charter to build the Conway & Seashore Railroad to transport timber from the coast to inland customers. The railroad began daily service on 1 May 1900, with two wood-burning locomotives. One of the engines was dubbed "The Black Maria" and came second-hand from a North Carolina logging operation.


title: Myrtle Beach, South Carolina

text: After the railroad was finished, employees of the lumber and railroad company would take train flatcars down to the beach area on their free weekends, becoming the first Grand Strand tourists. The railroad terminus was nicknamed "New Town", contrasting it with the "Old Town", or Conway.


title: Myrtle Beach, South Carolina

text: Around the start of the 20th century, Franklin Burroughs envisioned turning New Town into a tourist destination rivaling the Florida and northeastern beaches. Burroughs died in 1897, but his sons completed the railroad's expansion to the beach and opened the Seaside Inn in 1901.


title: Myrtle Beach, South Carolina

text: Around 1900, a contest was held to name the area, and Burroughs's wife suggested honoring the locally abundant shrub, the southern wax myrtle ("Myrica cerifera"). The Withers post office changed its name to "Myrtle Beach" soon afterward. It incorporated as a town in 1938 and as a city in 1957.


title: Myrtle Beach, South Carolina

text: In 1937, Myrtle Beach Municipal Airport was built. It was taken over by the United States Army Air Corps in 1940 and converted into a military base. Commercial flights began in 1976 and shared the runway for over 15 years until the air base closed in 1993. Since then the airport has been named Myrtle Beach International Airport. In 2010 plans to build a new terminal were approved. In 1940, Kings Highway was finally paved, giving Myrtle Beach its first primary highway.


title: Myrtle Beach, South Carolina

text: The Myrtle Heights-Oak Park Historic District, Myrtle Beach Atlantic Coast Line Railroad Station, Ocean Forest Country Club and Pleasant Inn are listed on the National Register of Historic Places. Also listed were the Chesterfield Inn, Rainbow Court and the Myrtle Beach Pavilion, all now demolished. The Gay Dolphin Gift Cove on the Boardwalk was built in 1946 and sells seashells and Myrtle Beach souvenirs. It claims to be the "nation's largest gift shop".


title: Myrtle Beach, South Carolina

text: Myrtle Beach has been separated from the continental United States since 1936 by the Intracoastal Waterway, forcing the city and area in general to develop within a small distance from the coast. In part due to this separation, the area directly northwest of Myrtle Beach, across the waterway, remained primarily rural for a while, whereas its northeastern and southwestern ends were bordered by other developed tourist towns, North Myrtle Beach and Surfside Beach. Since then, the inland portion of the Myrtle Beach area has developed dramatically.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is by highway southeast of Florence, South Carolina, northeast of Charleston, South Carolina, and southwest of Wilmington, North Carolina.


title: Myrtle Beach, South Carolina

text: According to the United States Census Bureau, the city has an area of , of which are land and , or 1.03%, are water.


title: Myrtle Beach, South Carolina

text: According to the Köppen climate classification, Myrtle Beach has a humid subtropical climate or Cfa – typical of the Gulf and South Atlantic states. The city enjoys abundant sunshine year-round with more than 2800 hours annually.


title: Myrtle Beach, South Carolina

text: The summer season is long, hot, and humid in Myrtle Beach. Average daytime highs are from and average night-time lows are near . The coastal location of Myrtle Beach mitigates daytime summer heat "somewhat" compared to inland areas of South Carolina: Thus, while nearby Florence averages 65 days annually with high temperatures of or higher – Myrtle Beach averages only 21. The Bermuda High pumps in humidity from the tropical Atlantic toward Myrtle Beach, giving summers a near-tropical feel in the city. The warm Atlantic Ocean reaches or higher in the summer months off Myrtle Beach, making for warm and sultry summer nights. Summer thunderstorms are common in the hot season in Myrtle Beach, and the summer months from June through September have the most precipitation. In summer, thunderstorms normally build during the heat of the day – followed by brief and intense downpours. On average, September is the wettest month, with August close behind, due to the combination of thunderstorms and tropical weather systems that peaks these months.


title: Myrtle Beach, South Carolina

text: Myrtle Beach has mostly mild winters of short duration: Average daytime highs range from and nighttime lows are in the from December through February. Winter temperatures vary more than summer temperatures in Myrtle Beach: Some winters can see several cold days with highs only in the upper 40s F (7–9 °C), while other winter days can see highs in the upper 60s and low 70s F (19–23 °C). Myrtle Beach averages 33 days annually with frost, though in some years less than 15 days will see frost. Snowfall is very rare in Myrtle Beach; however, at least a trace of snow falls a few times each decade. In February 2010, a rare of snow fell in Myrtle Beach. The spring (March, April and May) and fall (September, October and November) months are normally mild and sunny in Myrtle Beach, with high temperatures in the 60s and 70s. The beach season in Myrtle Beach normally runs from late April through late October. SST (Sea Surface Temperatures) are often in the lower 80's (26–28 °C) off South Carolina in summer and early fall.


title: Myrtle Beach, South Carolina

text: The temperature range measured in Myrtle Beach has historically ranged from a record summer heat of to the record winter cold of . In spite of the mild winter averages, ice days have been recorded, albeit rarely. The coldest daily maximum was in January 1962 whereas the normal year between 1991 and 2020 had the coldest maximum average of . Overnight lows can be extremely hot and muggy, although the record warm low of in July 1942 is some way above the means of for the warmest annual minimum.


title: Myrtle Beach, South Carolina

text: Summer thunderstorms are typically brief, but severe thunderstorms do occur on occasion. Tornadoes are rare, with the most significant event occurring in 2001 when multiple tornadoes touched down in the area. Tropical cyclones occasionally impact Myrtle Beach, though weaker tropical storms and weak tropical lows are more common. Like most areas prone to tropical cyclones, a direct hit by a major hurricane is infrequent in Myrtle Beach. The last hurricane to cause significant damage in Myrtle Beach was Hurricane Hugo in 1989. The worst hurricane in Myrtle Beach's history was Hurricane Hazel in 1954.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is the largest principal city of the Myrtle Beach-Conway-Georgetown CSA, a Combined Statistical Area that includes the Myrtle Beach-Conway-North Myrtle Beach metropolitan area (Horry County) and the Georgetown micropolitan area (Georgetown County), which had a combined population of 329,449 at the 2010 census.


title: Myrtle Beach, South Carolina

text: As of the 2020 United States census, there were 35,682 people, 13,817 households, and 7,678 families residing in the city.


title: Myrtle Beach, South Carolina

text: As of the 2010 census, the population of Myrtle Beach was 27,109. According to the 2000 census there were 22,759 permanent residents in Myrtle Beach, 10,413 households, 5,414 families, 1,356.5 people per square mile (523.7/km), with 14,658 housing units at an average density of 873.5 per square mile (337.3/km).


title: Myrtle Beach, South Carolina

text: Crime rate levels in Myrtle Beach are high compared to the rest of South Carolina. The FBI reported 583 cases of violent crime in the year 2016, of which 5 were murder, 46 were rape and 139 were robbery. Aggravated assault 348, property crime 4395, burglary 469, larceny theft 3555, motor vehicle theft 371, and arson 10 were also reported.


title: Myrtle Beach, South Carolina

text: The average number of crimes per thousand population is 0.16 murders, 1.43 rapes, 4.31 robberies and 10.83 assaults.


title: Myrtle Beach, South Carolina

text: Myrtle Beach's economy is dominated by the tourist industry; hotels, motels, resorts, restaurants, attractions, and retail developments exist in abundance to serve visitors.


title: Myrtle Beach, South Carolina

text: Hosting over 20 million visitors annually, the Grand Strand is home to an array of tourist attractions, and the area receives a large influx of visitors during all seasons. It is estimated that nearly 100,000 visitors a year are international travelers, including tourists from Canada, Germany and the United Kingdom.


title: Myrtle Beach, South Carolina

text: Myrtle Beach hosts a variety of special conventions, events, and musical concerts. The area's attractions include its beaches and courses, amusement parks, an aquarium, Legends in Concert, retail developments, shopping complexes and over 1,900 restaurants including seafood restaurants. The area also has dinner theaters, nightclubs, and many tourist shops. Myrtle Beach has approximately 425 hotels, with many on the beachfront, and approximately 157 accommodation units in total. The area is also home to over 80 golf courses and over 30 miniature golf courses. Live shows are offered year round at theaters including the Alabama Theatre, Carolina Opry, Asher Theater, Calvin Gilmore Theater, Legends in Concert, and Medieval Times Family Dinner Theater. Several shows offer special holiday themed shows.


title: Myrtle Beach, South Carolina

text: The Myrtle Beach Boardwalk opened in 2010 and has been recognized as the nation's #3 boardwalk by "National Geographic" and one of the best US boardwalks by Travel + Leisure magazine. The Myrtle Beach Skywheel opened at the boardwalk in May 2011, and is a observation wheel, similar to a ferris wheel, with glass gondolas that look over the Atlantic Ocean. This is the first wheel of its kind in the U.S. Myrtle Beach State Park, established in 1935, has just under a mile of Grand Strand beach and is a prime location for camping, swimming, hiking, biking, and fishing. Pier 14 by the Boardwalk.


title: Myrtle Beach, South Carolina

text: The Myrtle Beach Convention Center is a large facility that hosts a variety of meetings, conferences, exhibits, and special events every year. The expansive center, which opened in 2003, has a Sheraton hotel and resort.


title: Myrtle Beach, South Carolina

text: Each March since 1951 during Ontario's spring break, Myrtle Beach has hosted Canadian-American Days, also known as Can-Am Days. Tens of thousands of tourists flock to the area for a week's worth of special events. Myrtle Beach is also home to Coastal Uncorked, a food and wine festival held in the late spring annually. The city hosts Sun Fun Festival early each June. Later in June, Myrtle Beach is a popular destination for recently graduated high school seniors for Senior Week.


title: Myrtle Beach, South Carolina

text: Carolina Country Music Fest (CCMF) is an outdoor country music festival that takes place in June of each year and was founded in 2015 by Charlotte-based company Full House Productions. Due to concerns surrounding the coronavirus pandemic the festival wasn't held in 2020, but is scheduled to return in 2021 and take place on 10–13 June 2021.


title: Myrtle Beach, South Carolina

text: Myrtle Beach International Airport serves the city and surrounding area. With regular flights to and from destinations such as Atlanta, Boston, Detroit, Fort Lauderdale, New York and Washington, the airport is well connected for both domestic and international tourists. It also serves as a seasonal gateway to and from the likes of Chicago, Dallas and Toronto.


title: Myrtle Beach, South Carolina

text: The city is between Wilmington, North Carolina and Charleston, South Carolina with U.S. Route 17 serving as the main transport link for those journeying between those cities.


title: Myrtle Beach, South Carolina

text: Thongs (or any swimwear revealing any portion of the buttocks) are not permitted in public in Myrtle Beach, including all beaches. Violators of the ban may be arrested, jailed, or fined. The city's "thong ordinance" has been in effect since the 1990s.


title: Myrtle Beach, South Carolina

text: Myrtle Beach Bike Week, also called "Harley Bike Week", is a week-long motorcycle rally first held in 1940, the same year Kings Highway was paved. The event has attracted as many as 200,000 visitors to the city every May. Black Bike Week, founded in 1980, takes place the weekend around Memorial Day Weekend and is the largest African American motorcycle rally in the US and attracts as many as 400,000 visitors. The event was created in response to a history of discrimination against African-American visitors and riders to Myrtle Beach and the Grand Strand Area.


title: Myrtle Beach, South Carolina

text: The Myrtle Beach government created 15 new laws aimed at preventing all sanctioned motorcycle events within the city in response to controversy including accusations of racism by African-American riders during their event and complaints of lawlessness and poor behavior during all highly attended events. Several lawsuits by the National Association for the Advancement of Colored People (NAACP) against Myrtle Beach businesses were settled with agreements that discrimination cease, compensation be given to some plaintiffs, and employees be given diversity training. The NAACP suit against the City of Myrtle Beach was settled in 2006 without the city paying damages, but with the agreement police would use the same traffic control rules during both the black and the white motorcycle rallies.


title: Myrtle Beach, South Carolina

text: The South Carolina Supreme Court in June 2010 unanimously overturned one of the 15 ordinances, which had required all motorcyclists to wear helmets, on the grounds that the state law, requiring helmets only for riders under age 21, cannot be preempted by a city ordinance. In addition, the Court ruled that the ordinance created undue confusion, and that the city itself had invalidated their own helmet law and some other ordinances in a subsequent amendment. The law had been challenged by a group of motorcyclists and a group of Myrtle Beach businesses called BOOST, Business Owners Organized to Support Tourism, who opposed the city's anti-motorcycle tourism policy.


title: Myrtle Beach, South Carolina

text: The area is home to numerous golf courses and mini-golf courses along the Grand Strand and further inland. Myrtle Beach has been called the "Golf Capital of the World" because of the roughly 100 golf courses there, the record 4.2 million rounds played, and many miniature golf courses. 3.2 million total rounds of golf were played in 2017, down a "few hundred rounds" from a decade earlier. The number of golf courses more than doubled to over 120 over a 20-year period before declining late in the first decade of the 21st century. Tiger Woods declared Myrtle Beach "the mecca of golf" when visiting in 1997. The majority of the area's golf courses are public. The Grand Strand is home of "Hootie and the Blowfish Day After the Masters Tournament". Extensive Chinese investment to the Myrtle Beach area golf market has resulted in a significant surge of Chinese tourists to the area and also resulted in 25+ golf courses being owned and/or operated by Chinese nationals.


title: Myrtle Beach, South Carolina

text: Some of the notable golf courses and/or resorts include Barefoot Resort & Golf and TPC of Myrtle Beach.


title: Myrtle Beach, South Carolina

text: From 1998 to 2009 and again starting in 2011 (no Saturday races were held in 2010 due to snow), the area hosted the "Bi-Lo Myrtle Beach Marathon presented by Chick-Fil-A", every February featuring (since 2004) the Friday night Royal Bank of Canada 5K and the Saturday Dasani Half Marathon and Bi-Lo Marathon (from 1998 until 2008, a relay was held but dropped because of the popularity of the other events). Marathon day draws the limit of 6,000 runners annually (2,500 full, 3,500 half) and results usually in an unusual dawn as the race starts before dawn (6:30 am) in order to finish by 2:30 pm.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is home to the Myrtle Beach Pelicans, a Carolina League baseball team and a Chicago Cubs farm franchise. It was also home to the Myrtle Beach Mutiny, a pro soccer team playing in the Premier Development League until 2018.


title: Myrtle Beach, South Carolina

text: TicketReturn.com Field at Pelicans Ballpark is the home field of the Myrtle Beach Pelicans and is just off Highway 17 in Myrtle Beach. It opened in 1999 and seats 6,500 people. It is the finish point of the Bi-Lo Myrtle Beach Marathon. TicketReturn.com Field is also home of the annual "Baseball at the Beach" collegiate baseball tournament. Hosted by Coastal Carolina University each year, the tournament pits participating NCAA Division I baseball programs in the United States.


title: Myrtle Beach, South Carolina

text: NASCAR-sanctioned Stock car racing was held at Myrtle Beach Speedway, a , semi-banked, asphalt-paved oval track lon US 501. Drivers in the Late Model classes will compete (against those of Greenville-Pickens Speedway) for the South Carolina Championship in the NASCAR Whelen All-American Series. South Carolina Champions' scores will be calculated against other state and provincial champions for a continental championship.


title: Myrtle Beach, South Carolina

text: It hosted the 2010 UOA Nationals where 8 collegiate ultimate teams from 5 conferences will be represented.


title: Myrtle Beach, South Carolina

text: The city of Myrtle Beach has a council-manager government. The Mayor sits as a Council member-at-large and presides over City council meetings. If the Mayor cannot preside over a City Council meeting, the Mayor Pro-Tem is the presiding officer of the meeting until such time as the Mayor returns to the seat. The City Manager is responsible for the administration and the day-to-day operation of all of the municipal services and city departments. The City Manager also maintains intergovernmental relationships with federal, state, county and other local governments. The city of Myrtle Beach reformed into a council-manager government system in 1974 under the administration of Mayor Bob Hirsch and city manager David Stradinger, who moved away from the city's former strong-mayor form of government.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is served by a single public school district. Horry County Schools educates around 40,000 students and is the third largest school district in South Carolina.


title: Myrtle Beach, South Carolina

text: The Grand Strand and Florence, South Carolina, share a common defined market by Nielsen Media Research in Horry, Marion, Dillon, Darlington, Marlboro, Scotland, Robeson, and Florence counties. Two major stations are licensed to Myrtle Beach: NBC affiliate WMBF-TV 32 and Fox affiliate WFXB 43. Myrtle Beach is also served by PBS member stations WHMC/WJPM-TV 23/33, licensed respectively to Conway and Florence, and three commercial stations licensed to Florence: CBS affiliate WBTW 13 (with MyNetworkTV on DT2), ABC affiliate WPDE-TV 15, and CW affiliate WWMB 21.


title: Myrtle Beach, South Carolina

text: "The Sun News" has traditionally been the largest daily paper published along the Grand Strand, with a readership base extending from Georgetown, South Carolina, to Sunset Beach, North Carolina. The paper has been in existence since the 1930s and was formerly published by Knight Ridder before that company was bought by The McClatchy Company. Like many newspapers, the paper has declined in recent years due to shifts in readership and financial pressures at its parent company. It stopped local printing operations and downsized its newsroom in May 2020.


title: Myrtle Beach, South Carolina

text: Myrtle Beach is also served by "The Myrtle Beach Herald", a weekly newspaper that is part of the Waccamaw Publishers group. It is locally owned by Steve and Cheryl Robertson. "The Herald" also produces a newspaper targeted at tourists called " Visit!".


title: Myrtle Beach, South Carolina

text: In 2020, Charleston-based "The Post and Courier" set up an official bureau in Myrtle Beach, after years of attempting to move into the market and purchasing "The Georgetown Times", which it merged with the new operation.


title: Myrtle Beach, South Carolina

text: Grand Strand Medical Center (GSMC) is a 369-bed acute care hospital and Level 1 Adult Trauma Center known for its programs in cardiology, heart surgery, and stroke treatment. It was opened on 21 April 1978 to succeed the former Ocean View Memorial Hospital (1958-1978), the first major hospital in Myrtle Beach. GSMC contains the only cardiac surgery and neurosurgery programs in the greater Myrtle Beach area and was a recipient of the Healthgrades 100 Best Hospitals for Cardiac Surgery in 2012 and 2013. As a teaching hospital, Grand Strand Medical Center is the home of ACGME accredited residency training programs (internal medicine, general surgery, emergency medicine, and family medicine), and hosts rotating medical students from the University of South Carolina and Edward Via College of Osteopathic Medicine (VCOM). Over 270 physicians and 1,400 staff serve at the facility.


title: Myrtle Beach, South Carolina

text: The Waccamaw Coast Line Railroad is a short-line railroad division of the Baltimore and Annapolis Railroad, extending from a connection with the Carolina Southern Railroad, another division of that company, at Conway to Myrtle Beach. The line was opened in 1900 by the Conway Coast and Western Railroad, a predecessor of the Atlantic Coast Line Railroad. The Seaboard System Railroad sold the line to Horry County in November 1985, and it was operated by the Horry County Railway until October 1987, when the WCLR took over. The Carolina Southern Railroad acquired the WCLR in September 1995, and since then it has been a division of the Baltimore and Annapolis Railroad. Horry County owns the line but leased it to the Carolina Southern Railroad in 2000.


title: Myrtle Beach, South Carolina

text: Carolina Southern Railroad is a short line rail operator running on less than of rail at a maximum speed of . It transports mostly freight brought to it from national rail operators. The company makes one scheduled delivery per month into the City of Myrtle Beach. It is off of Main Street in Conway, South Carolina, and is one of the few remaining train depots in South Carolina. It has been painstakingly restored to its former glory and the Carolina Southern Railroad has become one of the frequent destinations for freight services as well as passenger cars and observational locomotives. The railroad was originally erected in late 1886 and the first train steamed into the Conway Depot in December 1887.


title: Myrtle Beach, South Carolina

text: The Carolina Southern Railroad stands as a permanent landmark in Southern History. Carolina Southern Railroad is a member of the Carolina Rails system with connections that run from Whiteville, North Carolina, to Mullins, South Carolina, and also from Chadbourn, North Carolina, to Conway. Carolina Southern railroad is also responsible for operation of the Waccamaw Coast Line Railroad, which is a railway that runs from Conway to Myrtle Beach.


title: Myrtle Beach, South Carolina

text: On August 30, 2011, Carolina Southern Railroad voluntary shut down because several bridges along the rail were overdue for maintenance. The shutdown caused Carolina Southern Railroad to lay off nearly all of its employees. On May 24, 2012, the Federal Railroad Administration (FRA) commenced a bridge inspection on the CSR and the Waccamaw Coastline Railroad (the Horry County portion of rail). Fifty-two of 187 bridges were inspected and seven had critical defects. On May 26, 2011, the CSR voluntarily ceased operation, so that they could bring in a certified bridge engineer to inspect the seven critical bridges and prepare a plan for their repairs. Based on the engineer's recommendations, CSR made the necessary repairs on the bridges and CSR resumed operations August 8, 2011. The FRA returned to inspect the bridges and made a recommendation that CSR cease operations until all bridge repairs were completed. There are efforts to bring the railroad back online.


title: Myrtle Beach, South Carolina

text: In 2015, railroad operator RJ Corman acquired the former CSR line and re-opened it freight service in early April 2016.


title: Myrtle Beach, South Carolina

text: Until 1955 the Atlantic Coast Line Railroad ran passenger rail service from the Myrtle Beach Station to Chadbourn, where a connection could be made to interstate ACL train service.


title: Myrtle Beach, South Carolina

text: Within the last decade, new roads have been created to ease congestion caused by the yearly influx of visitors. Most of these roads follow the Metro Loop Road Plan, organized in 1997 to improve the traffic flow of Myrtle Beach. Some of the roads included have either been funded through Road Improvement Development Effort (RIDE I) funding or through the City of Myrtle Beach.


title: Myrtle Beach, South Carolina

text: RIDE II plans include the third phase of S.C. Highway 31, a graded separation of Farrow Parkway and US 17 Bypass at the back gate of the former Air Force base, and many other projects. The county is debating where to allocate the $400 million generated through a proposed 1-cent sales tax. Other road projects in Horry County, including some in Aynor and Conway, will be included when voted upon.


title: Myrtle Beach, South Carolina

text: Plans exist for Myrtle Beach to be served by two interstates, Interstate 73 and Interstate 74. The Robert Edge Parkway will connect I-74 to downtown North Myrtle Beach.


title: 2021 NBA playoffs

text: The 2021 NBA playoffs was the postseason tournament of the National Basketball Association's 2020–21 season. With the COVID-19 pandemic impacting the NBA for the second consecutive year, the regular season was reduced to 72 games for each team and the start date of the playoffs was moved from its usual time in mid-April to May 22, 2021. It ended with the 2021 NBA Finals in July.


title: 2021 NBA playoffs

text: The 2021 NBA Finals matchup featured the Milwaukee Bucks and the Phoenix Suns. Game 1 of the series was played on July 6, where the Suns took down the Bucks 118–105. Game 2 was played on July 8 at the Phoenix Suns Arena (now called Footprint Center) and ended with a score of 118–108 in favor of the Suns. The Bucks won the NBA Finals in six games after being down 0–2, their first championship since 1971.


title: 2021 NBA playoffs

text: Both the defending champion Los Angeles Lakers and the 2020 NBA Finals runner-up Miami Heat lost in the first round to the eventual finalists: the Phoenix Suns and the Milwaukee Bucks, respectively. The Suns advanced to their first NBA Finals since 1993 after winning the Western Conference Finals against the Los Angeles Clippers in six games; the Bucks also won the Eastern Conference Finals in six games, against the Atlanta Hawks to reach their first NBA Finals since 1974.


title: 2021 NBA playoffs

text: It was the first year the NBA used a 20-team playoff, with a two-stage system in both conferences, with 16 of the 20 teams advancing to the second stage. The first stage, the NBA Play-In Games, was a four-team playoff in each conference for the No. 7 to No. 10 seeds in each conference. In this format, the No. 7 and No. 8 teams need to win one game to advance to the second stage, with a double chance, while the No. 9 and No. 10 teams need to win two games to advance, eliminated by just one loss.


title: 2021 NBA playoffs

text: The NBA Board of Governors approved a format for the 2020–21 season to have a play-in tournament involving the teams that ranked 7th through 10th in each conference. The 7th place team and 8th place team participate in the double-chance game, with the winner advancing to the playoffs as the 7-seed. The loser then plays the winner of the elimination game between the 9th place and 10th place teams to determine the playoff's 8-seed. The NBA's regular playoff format would then proceed as normal.


title: 2021 NBA playoffs

text: Under the NBA's regular playoff format, the eight teams with the most wins in each conference qualified for the playoffs. The seedings were based on each team's record. Each conference's bracket was fixed; there was no reseeding. All rounds were best-of-seven series; the series ended when one team won four games, and that team advanced to the next round. All rounds, including the NBA Finals, were in a 2–2–1–1–1 format. In the conference playoffs, home court advantage went to the higher-seeded team (number one being the highest). Seeding was based on each team's regular season record within a conference; if two teams had the same record, standard tiebreaker rules were used. Conference seedings were ignored for the NBA Finals: Home court advantage went to the team with the better regular season record, and, if needed, ties were broken based on head-to-head record, followed by intra-conference record.


title: 2021 NBA playoffs

text: On April 25, 2021, the Utah Jazz became the first team to clinch a playoff spot. While noted in the below tables, division titles have no bearing on seeding.


title: 2021 NBA playoffs

text: Indiana (34–38) and Charlotte (33–39) also secured play-in berths but did not advance to the playoffs.


title: 2021 NBA playoffs

text: Golden State (39–33) and San Antonio (33–39) also secured play-in berths but did not advance to the playoffs.


title: 2021 NBA playoffs

text: Teams in bold advanced to the next round. The numbers to the left of each team indicate the team's seeding in its conference, and the numbers to the right indicate the number of games the team won in that round. The division champions are marked by an asterisk. Teams with home court advantage, the higher seeded team, are shown in italics.


title: 2021 NBA playoffs

text: This was the sixth playoff meeting between these two teams, with the 76ers winning three of the first five meetings.


title: 2021 NBA playoffs

text: This was the third playoff meeting between these two teams, but the first since the New Jersey Nets relocated to Brooklyn and became the Brooklyn Nets in 2012, with the Nets winning the first two meetings.


title: 2021 NBA playoffs

text: The Bucks struggled offensively against Miami, shooting only 16% (5–31) on three-point shots. The game went into overtime thanks to a game-tying, buzzer-beating layup by Jimmy Butler, but Milwaukee was able to pull away and win on a Khris Middleton jump shot, made with only 0.5 seconds left.


title: 2021 NBA playoffs

text: The Bucks erupted for 46 points in the first quarter, setting a new franchise playoff record, en route to a dominating 132–98 victory. The Bucks would make 22 three-pointers, after making only 5 in game 1.


title: 2021 NBA playoffs

text: The Bucks would cruise to another convincing victory in game 3, to take a commanding 3–0 series lead on Miami. In games 2 & 3, the Heat led for only :17, out of 96 minutes of game time.


title: 2021 NBA playoffs

text: Though Miami built a 7-point lead at halftime, the Bucks went on a 24–6 run in the third quarter to take a lead they would not relinquish, leading to a four-game sweep of the Heat.


title: 2021 NBA playoffs

text: This was the third playoff meeting between these two teams, with the Heat winning the first two meetings.


title: 2021 NBA playoffs

text: This was the third playoff meeting between these two teams, with the Knicks winning the first two meetings.


title: 2021 NBA playoffs

text: This was the 13th playoff meeting between these two teams, with the Lakers winning eight of the first 12 meetings.


title: 2021 NBA playoffs

text: This was the fourth playoff meeting between these two teams, with Portland winning two of the first three meetings.


title: 2021 NBA playoffs

text: This was the second playoff meeting between these two teams, with the Clippers winning the first meeting.


title: 2021 NBA playoffs

text: The Atlanta Hawks dominated during the early part of the game, leading by as much as 26 points, The 76ers however performed a major rally, eventually cutting the deficit to just 3 points with a minute left in Regulation, 20 seconds of game time later however Bogdan Bogdanovic would hit a clutch 3, the 76ers' would make it a 3-point game again with 28.7 seconds left, Joel Embiid then later committed a clear path foul, thus not only giving Atlanta 2 free throws, but possession of the ball, the Hawks would seal the game when Trae Young gave an alley-oop assist to John Collins.


title: 2021 NBA playoffs

text: Trae Young secured a double-double with 35 points & 10 assists for The Hawks. Joel Embiid scored 39 points for the 76ers.After the 76ers' Started the game up 20–4 with 6 minutes left in the 1st quarter, the Hawks rallied and the game remained close until the end of the 3rd quarter in which the 76ers' blew the game open with a 14–0 run at one point, resulting in the series being tied at a game apiece.


title: 2021 NBA playoffs

text: Joel Embiid secured a double-double with 40 points & 13 rebounds, while Danny Green passed 8 assists. Trae Young also scored a double-double with 21 points & 11 assists while John Collins grabbed 10 rebounds.The 76ers' Cruised their way to victory throughout the entire game thanks in part to Joel Embiid's 27 points, 9 rebounds, & 8 assists.


title: 2021 NBA playoffs

text: Trae Young Scored 28 points & 8 assists in the losing effort for the hawks.Despite being down by 18, the Atlanta hawks staged a comeback, eventually taking their first lead since it was 10–12 in the 1st quarter, by the start of the 4th quarter. the game remained deadlocked for the rest of the game, as the 76ers' were up by 4 with 2:20 left in the 4th quarter, the Hawks responded with a 7–0 run, leading by 3 with 49.6 seconds left, after Embiid got fouled & made both free throws to make it 101-100 and a turnover by John Collins, The 76ers' had a chance at leading the series 3 games to 1, Embiid's go-ahead shot fell short and the ball went out-of-bounds last touched by Ben Simmons, giving Atlanta the ball with 8.2 seconds left.


title: 2021 NBA playoffs

text: After Trae Young made both of his free throws to make it a 3-point game, the sixers had 6.6 seconds left to Tie it, but Seth Curry's Game-tying 3-pointer was no good, giving Atlanta the comeback victory.In the pivotal Game 5, The 76ers' appeared to be on their way to victory, leading by as much as 26 points and with a 99.7% win probability according to ESPN. However the Hawks, who came back from 18 down in the last game, performed one of the most memorable comebacks in NBA Playoff history. At one point, the Sixers were still up 104–94 with 4 minutes left in the game, only for the hawks to respond with a 13–0 run to make it a 3-point lead with 50 seconds left in the 4th quarter in what was their First lead of the entire game.


title: 2021 NBA playoffs

text: The Climax of the game came with 12 seconds left, after a blocking foul by Danilo Gallinari, which sent Joel Embiid To the line, he would miss both free throws and Atlanta then had possession of the ball. Later on, Trae Young would seal it with 2 clutch free throws, Seth Curry then made a meaningless basket to make the final score 109–106 in favor the Hawks, who were now one game away from their first conference finals birth since 2015. Once the final buzzer sounded, the 76ers' faithful booed their entire team off the floor due to the collapse.


title: 2021 NBA playoffs

text: The Hawks' Became the 6th team in NBA Playoffs history to win a playoff game after trailing by 18+ points entering the 4th quarter in the shot clock eraWith the Hawks looking to advance to the Eastern Conference finals at their home floor, they would lead by as much as 12 points during the 2nd quarter, But the 76ers' who were trying to stave off elimination after back-to-back collapses, managed to take control of the game.


title: 2021 NBA playoffs

text: However, the game once again would go down to the wire, as the Sixers were up 94–87 with 3 minutes left, the Hawks' responded with 2 Three-pointers from Gallinari & Young, who cut the deficit to one with 1:59 left in the 4th quarter. The Lights at State Farm Arena would then go out, causing a delay for one minute, once the lights came back on, Philadelphia immediately responded by preserving the lead as Tobias Harris would make 2 Game-sealing Free throws to send the series back to Philadelphia for Game 7 on Sunday Night.In Front of a ruckus Wells Fargo Center, Game 7 was a deadlocked affair, with neither team able to gain a double-digit lead. The Game & The Series would once again, come down to the wire, with 1:12 left in the 4th quarter, The Hawks were leading 93-92 and had the ball. in the climax of the game, Kevin Huerter attempted a 3-point shot that missed, but was fouled by Matisse Thybulle, sending him to the line where he would make 3 free-throws. On the next possession, Danilo Gallinari stripped Joel Embiid of the ball, who then dunked to make it 98–92 in Favor of the hawks, from that point on, the Game was over as the Atlanta Hawks upset the top-seeded 76ers to advance to the Eastern conference finals for the first time in 6 years.


title: 2021 NBA playoffs

text: Kevin Huerter became the Hawks' top scorer with 27 points, John Collins grabbed 16 rebounds & Trae Young passed 10 assists.


title: 2021 NBA playoffs

text: Ben Simmons' Game 7 Performance was Criticized, he scored only 5 points despite passing 13 assists, at the 3:30 mark of the 4th quarter with the sixers down 2, Simmons would pass a wide open basket to Matisse Thybulle, who in turn got fouled and split the free throws. Sixers' Coach Doc Rivers was asked in his post-game conference if Simmons could be the point guard of a championship team, Rivers Responded with "I Don't know the answer to that right now". Joel Embiid cited the decision as the turning point of the game.


title: 2021 NBA playoffs

text: Eventually it would be Ben Simmons, Andre Drummond, & Seth Curry's last playoff game as a 76er, for which all of them would be traded to the Brooklyn Nets on February 10, 2022.


title: 2021 NBA playoffs

text: This was the third playoff meeting between these two teams, with the 76ers winning both previous meetings.


title: 2021 NBA playoffs

text: Game 7 would go on to be an instant classic with both teams locked in for the entire game. In the final seconds of regulation, Kevin Durant appeared to have given the Nets a 1-point lead on a fadeaway three-point shot with 1 second left. Replay showed, however, that his foot was on the line. With the score tied at 109, Milwaukee had a chance to win the series, but Giannis Antetokounmpo's turnaround jump shot missed, sending the game into overtime. The Nets held a two-point lead until the final 90 seconds of overtime where the Bucks would score on back-to-back possessions to get on the board and take a 113–111 lead with 40 seconds remaining. The Nets had possession in the last 15 seconds of the game, concluding with yet another game-tying, almost-three-point jump shot attempt by Durant; however, it was all air. The Bucks subsequently sealed the game on two free throws by Brook Lopez (a former Net), sending them to the Eastern Conference Finals for the second time in three years. This marked the first game seven to go into overtime since 2006 involving the Dallas Mavericks and the San Antonio Spurs, which the Mavericks won and prevented the team from blowing a 3–1 lead to the Spurs. It was also the Bucks' first victory on the road in a postseason game seven, having gone 0–7 in previous playoff road game seven's. It was also became the sixth team in NBA playoff history and the first since the 2017–18 Cleveland Cavaliers that a road team won game seven in the postseason also joined by other teams the 1968–69 Boston Celtics (who upset the Los Angeles Lakers in the 1969 series.), 1970–71 Baltimore Bullets (who were swept by eventual champions Bucks in the 1971 series.), the 2006–07 Utah Jazz, 2007–08 San Antonio Spurs and 2017–18 Golden State Warriors, and also the third team in NBA playoff history to win game seven on the road in overtime joined the 2001–02 Los Angeles Lakers, and the 2005–06 Mavericks' team.


title: 2021 NBA playoffs

text: This was the fourth playoff meeting between these two teams, but the first since the New Jersey Nets relocated to Brooklyn and became the Brooklyn Nets in 2012, with the Bucks winning two of the first three meetings.


title: 2021 NBA playoffs

text: The Clippers were trailing by 22 at the end of the first half in Game 6. They went down 25 at the start of the third quarter, before a retaliation led by Terance Mann allowed the Clippers to fight back to within 3 points at the end of the third quarter. In the fourth, the momentum from the third quarter and Utah's struggles allowed the Clippers to complete the comeback, becoming the first team to recover from being down 0–2 twice in the same playoffs, and reaching their first Conference Finals in franchise history.


title: 2021 NBA playoffs

text: This was the fourth playoff meeting between these two teams, with the Jazz winning the previous three meetings.


title: 2021 NBA playoffs

text: This was the fourth playoff meeting between these two teams, with Phoenix winning two of the first three meetings.


title: 2021 NBA playoffs

text: Atlanta's top offensive star, Trae Young, scored 48 points in his conference finals debut, while the Hawks rallied in the 2nd half to beat the Bucks in game 1 in Milwaukee, aided by 5 offensive rebounds in the final 2 minutes.


title: 2021 NBA playoffs

text: Trailing by 2 points going into the 4th quarter, the Bucks' Khris Middleton would carry Milwaukee to victory in game 3, outscoring Atlanta in the final quarter by himself, 20–17, en route to a game-high 38 points, putting the Bucks back in the lead in the series and getting back homecourt advantage. Atlanta's loss was also compounded when Trae Young suffered a bruised foot when he rolled his ankle over a referee's foot, leaving his status for the rest of the series in doubt.


title: 2021 NBA playoffs

text: The Bucks' 3-point woes returned in game 4, as the team only shot 21% (8–39) in a loss to Atlanta that evened the series once more. Even worse, the Bucks' superstar, Giannis Antetokounmpo, hyperextended his knee while trying to defend an alley-oop dunk, though an MRI the following day revealed no structural damage, and Antetokounmpo potentially available for either game 7 or the NBA Finals.


title: 2021 NBA playoffs

text: With both teams' stars out with injuries, both the Hawks and Bucks needed contributions from their other players in game 5. The Bucks would deliver, led by Brook Lopez's 33 points. In addition to Lopez, 3 other Bucks starters (Khris Middleton, Jrue Holiday, and Bobby Portis) scored at least 20 points. While Atlanta kept the game close, aided by Bogdan Bogdanovic's 28 points, the Bucks took a 3–2 series lead, leaving them one win away from the Eastern Conference championship.


title: 2021 NBA playoffs

text: Facing elimination, the Hawks got Trae Young back to start game 6, but he still struggled with his injured foot, scoring only 14 points. After leading Atlanta by only 4 points at halftime, Khris Middleton would score the Bucks' first 16 points of the 3rd quarter to build a 19-point lead going into the 4th quarter. The Bucks would weather a wave of hot shooting from Bogdan Bogdanovic and Cam Reddish, helped by a crucial 3-point shot by PJ Tucker, and an alley-oop dunk by Brook Lopez that essentially clinched the game and the series for the Bucks. The victory gave the Bucks the Eastern Conference championship, their 3rd overall conference title (though the previous two were for the Western Conference), and their first trip to the NBA Finals since 1974.


title: 2021 NBA playoffs

text: This was the fifth playoff meeting between these two teams, with each team winning two series apiece. Four months later, two teams from Milwaukee and Atlanta would meet again in a sports postseason as the Braves beat the Brewers in the 2021 NLDS.


title: 2021 NBA playoffs

text: The Clippers shot 0–12 in the fourth quarter on shots that could have tied the game or taken the lead. That is the most such attempts without a make in the fourth quarter of a game over the last 25 postseasons. During the last 8 seconds of the game when the Clippers trailed 1 point, there was a controversial call where Nicolas Batum of the Clippers deflected the ball off the finger tips of Cameron Payne of the Suns, but the ball was given to the Suns. There was no review of the play despite a heavy plea from the Clippers.


title: 2021 NBA playoffs

text: This was the second playoff meeting between these two teams, with the Bucks winning the first meeting.


title: 2021 NBA playoffs

text: ESPN, ABC, TNT, and NBA TV broadcast the playoffs nationally in the United States. During the first two rounds, games were split by ESPN, ABC and TNT. TNT primarily aired games on Saturday through Wednesday, while ESPN on Friday and Saturday. For Thursday games, TNT had them in the first round and ESPN in the second round. ABC then aired selected first and second-round games on Friday through Sunday. NBA TV also televised selected games in the first round on Tuesday through Thursday. Regional sports networks affiliated with teams also broadcast the games, except for weekend games televised on ABC. ESPN/ABC had exclusive coverage of the Western Conference Finals while TNT had exclusive coverage of the Eastern Conference Finals. ABC had exclusive coverage of the NBA Finals for the 19th straight year.


title: 2021 NBA playoffs

text: This was the final postseason for Marv Albert, who announced his retirement on May 17, 2021. Albert, who turned 80 in June, has spent most of the last 31 years as the lead broadcaster for NBA coverage on TNT and NBC.


title: Bohr model

text: In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. It came after the solar system Joseph Larmor model (1897), the solar system Jean Perrin model (1901), the cubical model (1902), the Hantaro Nagaoka Saturnian model (1904), the plum pudding model (1904), the quantum Arthur Haas model (1910), the Rutherford model (1911), and the nuclear quantum John William Nicholson model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation introduced by Haas and Nicholson, but forsaking any attempt to align with classical physics radiation.


title: Bohr model

text: The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results.


title: Bohr model

text: The Bohr model is a relatively primitive model of the hydrogen atom, compared to the "valence shell atom" model. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics or energy level diagrams before moving on to the more accurate, but more complex, valence shell atom. A related quantum model was originally proposed by Arthur Erich Haas in 1910 but was rejected until the 1911 Solvay Congress where it was thoroughly discussed. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a mature quantum mechanics (1925) is often referred to as the old quantum theory.


title: Bohr model

text: In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford naturally considered a planetary model of the atom, the Rutherford model of 1911. This had electrons orbiting a solar nucleus, but involved a technical difficulty: the laws of classical mechanics (i.e. the Larmor formula) predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. Rutherford's atom model is disastrous because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency due to the orbital period becoming shorter, resulting in electromagnetic radiation with a continuous spectrum. However, late 19th-century experiments with electric discharges had shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies. By the early twentieth century, it was expected that the atom would account for the spectral lines. In 1897, Lord Rayleigh analyzed the problem. By 1906, Rayleigh said, “the frequencies observed in the spectrum may not be frequencies of disturbance or of oscillation in the ordinary sense at all, but rather form an essential part of the original constitution of the atom as determined by conditions of stability.”


title: Bohr model

text: The outline of Bohr's atom came during the proceedings of the first Solvay Conference in 1911 on the subject of Radiation and Quanta, at which Bohr's mentor, Rutherford was present. Max Planck’s lecture ended with this remark: “... atoms or electrons subject to the molecular bond would obey the laws of quantum theory”. Hendrik Lorentz in the discussion of Planck's lecture raised the question of the composition of the atom based on Thomson's model with a great portion of the discussion around the atomic model developed by Arthur Erich Haas. Lorentz explained that Planck's constant could be taken as determining the size of atoms, or that the size of atoms could be taken to determine Planck's constant. Lorentz included comments regarding the emission and absorption of radiation concluding that “A stationary state will be established in which the number of electrons entering their spheres is equal to the number of those leaving them.” In the discussion of what could regulate energy differences between atoms, Max Planck simply stated: “The intermediaries could be the electrons.” The discussions outlined the need for the quantum theory to be included in the atom and the difficulties in an atomic theory. Planck in his talk said explicitly: “In order for an oscillator [molecule or atom] to be able to provide radiation in accordance with the equation, it is necessary to introduce into the laws of its operation, as we have already said at the beginning


title: Bohr model

text: of this Report, a particular physical hypothesis which is, on a fundamental point, in contradiction with classical Mechanics, explicitly or tacitly.” Bohr's first paper on his atomic model quotes Planck almost word for word, saying: “Whatever the alteration in the laws of motion of the electrons may be, it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, i. e. Planck's constant, or as it often is called the elementary quantum of action.” Bohr's footnote at the bottom of the page is to the French translation of the 1911 Solvay Congress proving he patterned his model directly on the proceedings and fundamental principles laid down by Planck, Lorentz, and the quantized Arthur Haas model of the atom which was mentioned seventeen times. Lorentz ended the discussion of Einstein's talk explaining: “The assumption that this energy must be a multiple of formula_1 leads to the following formula, where formula_2 is an integer: formula_3.” Rutherford could have outlined these points to Bohr or given him a copy of the proceedings since he quoted from them and used them as a reference. In a later interview, Bohr said it was very interesting to hear Rutherford's remarks about the Solvay Congress. But Bohr said, “I saw the actual reports” of the Solvay Congress.


title: Bohr model

text: Then in 1912, Bohr came across the John William Nicholson theory of the atom model that quantized angular momentum as "h"/2. According to a centennial celebration of the Bohr atom in Nature magazine, it was Nicholson who discovered that electrons radiate the spectral lines as they descend towards the nucleus and his theory was both nuclear and quantum. Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom. The importance of the work of Nicholson's nuclear quantum atomic model on Bohr's model has been emphasized by many historians.


title: Bohr model

text: Next, Bohr was told by his friend, Hans Hansen, that the Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885 that described wavelengths of some spectral lines of hydrogen. This was further generalized by Johannes Rydberg in 1888 resulting in what is now known as the Rydberg formula.


title: Bohr model

text: To overcome the problems of Rutherford's atom, in 1913 Niels Bohr put forth three postulates that sum up most of his model:


title: Bohr model

text: Bohr's condition, that the angular momentum is an integer multiple of "ħ" was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit:


title: Bohr model

text: According to de Broglie's hypothesis, matter particles such as the electron behave as waves. The of an electron is


title: Bohr model

text: where formula_10 is the angular momentum of the orbiting electron. Writing formula_11 for this angular momentum, the previous equation becomes


title: Bohr model

text: Bohr described angular momentum of the electron orbit as 1/2h while de Broglie's wavelength of described h divided by the electron momentum. In 1913, however, Bohr justified his rule by appealing to the correspondence principle, without providing any sort of wave interpretation. In 1913, the wave behavior of matter particles such as the electron was not suspected.


title: Bohr model

text: In 1925, a new kind of mechanics was proposed, quantum mechanics, in which Bohr's model of electrons traveling in quantized orbits was extended into a more accurate model of electron motion. The new theory was proposed by Werner Heisenberg. Another form of the same theory, wave mechanics, was discovered by the Austrian physicist Erwin Schrödinger independently, and by different reasoning. Schrödinger employed de Broglie's matter waves, but sought wave solutions of a three-dimensional wave equation describing electrons that were constrained to move about the nucleus of a hydrogen-like atom, by being trapped by the potential of the positive nuclear charge.


title: Bohr model

text: The Bohr model gives almost exact results only for a system where two charged points orbit each other at speeds much less than that of light. This not only involves one-electron systems such as the hydrogen atom, singly ionized helium, and doubly ionized lithium, but it includes positronium and Rydberg states of any atom where one electron is far away from everything else. It can be used for K-line X-ray transition calculations if other assumptions are added (see Moseley's law below). In high energy physics, it can be used to calculate the masses of heavy quark mesons.


title: Bohr model

text: If an electron in an atom is moving on an orbit with period "T", classically the electromagnetic radiation will repeat itself every orbital period. If the coupling to the electromagnetic field is weak, so that the orbit doesn't decay very much in one cycle, the radiation will be emitted in a pattern which repeats every period, so that the Fourier transform will have frequencies which are only multiples of 1/"T". This is the classical radiation law: the frequencies emitted are integer multiples of 1/"T".


title: Bohr model

text: In quantum mechanics, this emission must be in quanta of light, of frequencies consisting of integer multiples of 1/"T", so that classical mechanics is an approximate description at large quantum numbers. This means that the energy level corresponding to a classical orbit of period 1/"T" must have nearby energy levels which differ in energy by "h"/"T", and they should be equally spaced near that level,


title: Bohr model

text: Bohr worried whether the energy spacing 1/"T" should be best calculated with the period of the energy state formula_18, or formula_19, or some average—in hindsight, this model is only the leading semiclassical approximation.


title: Bohr model

text: Bohr considered circular orbits. Classically, these orbits must decay to smaller circles when photons are emitted. The level spacing between circular orbits can be calculated with the correspondence formula. For a Hydrogen atom, the classical orbits have a period "T" determined by Kepler's third law to scale as "r". The energy scales as 1/"r", so the level spacing formula amounts to


title: Bohr model

text: It is possible to determine the energy levels by recursively stepping down orbit by orbit, but there is a shortcut.


title: Bohr model

text: The angular momentum "L" of the circular orbit scales as formula_21. The energy in terms of the angular momentum is then


title: Bohr model

text: Assuming, with Bohr, that quantized values of "L" are equally spaced, the spacing between neighboring energies is


title: Bohr model

text: This is as desired for equally spaced angular momenta. If one kept track of the constants, the spacing would be "ħ", so the angular momentum should be an integer multiple of "ħ",


title: Bohr model

text: An electron in the lowest energy level of hydrogen () therefore has about 13.6 eV less energy than a motionless electron infinitely far from the nucleus. The next energy level () is −3.4 eV. The third (3) is −1.51 eV, and so on. For larger values of "n", these are also the binding energies of a highly excited atom with one electron in a large circular orbit around the rest of the atom. The hydrogen formula also coincides with the Wallis product.


title: Bohr model

text: Since this derivation is with the assumption that the nucleus is orbited by one electron, we can generalize this result by letting the nucleus have a charge , where "Z" is the atomic number. This will now give us energy levels for hydrogenic (hydrogen-like) atoms, which can serve as a rough order-of-magnitude approximation of the actual energy levels. So for nuclei with "Z" protons, the energy levels are (to a rough approximation):


title: Bohr model

text: The actual energy levels cannot be solved analytically for more than one electron (see "n"-body problem) because the electrons are not only affected by the nucleus but also interact with each other via the Coulomb Force.


title: Bohr model

text: When "Z" = 1/"α" (), the motion becomes highly relativistic, and "Z" cancels the "α" in "R"; the orbit energy begins to be comparable to rest energy. Sufficiently large nuclei, if they were stable, would reduce their charge by creating a bound electron from the vacuum, ejecting the positron to infinity. This is the theoretical phenomenon of electromagnetic charge screening which predicts a maximum nuclear charge. Emission of such positrons has been observed in the collisions of heavy ions to create temporary super-heavy nuclei.


title: Bohr model

text: The Bohr formula properly uses the reduced mass of electron and proton in all situations, instead of the mass of the electron,


title: Bohr model

text: However, these numbers are very nearly the same, due to the much larger mass of the proton, about 1836.1 times the mass of the electron, so that the reduced mass in the system is the mass of the electron multiplied by the constant 1836.1/(1+1836.1) = 0.99946. This fact was historically important in convincing Rutherford of the importance of Bohr's model, for it explained the fact that the frequencies of lines in the spectra for singly ionized helium do not differ from those of hydrogen by a factor of exactly 4, but rather by 4 times the ratio of the reduced mass for the hydrogen vs. the helium systems, which was much closer to the experimental ratio than exactly 4.


title: Bohr model

text: For positronium, the formula uses the reduced mass also, but in this case, it is exactly the electron mass divided by 2. For any value of the radius, the electron and the positron are each moving at half the speed around their common center of mass, and each has only one fourth the kinetic energy. The total kinetic energy is half what it would be for a single electron moving around a heavy nucleus.


title: Bohr model

text: The Rydberg formula, which was known empirically before Bohr's formula, is seen in Bohr's theory as describing the energies of transitions or quantum jumps between orbital energy levels. Bohr's formula gives the numerical value of the already-known and measured the Rydberg constant, but in terms of more fundamental constants of nature, including the electron's charge and the Planck constant.


title: Bohr model

text: When the electron gets moved from its original energy level to a higher one, it then jumps back each level until it comes to the original position, which results in a photon being emitted. Using the derived formula for the different energy levels of hydrogen one may determine the wavelengths of light that a hydrogen atom can emit.


title: Bohr model

text: The energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels:


title: Bohr model

text: This is known as the Rydberg formula, and the Rydberg constant is , or in natural units. This formula was known in the nineteenth century to scientists studying spectroscopy, but there was no theoretical explanation for this form or a theoretical prediction for the value of , until Bohr. In fact, Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman ( =1), Balmer ( =2), and Paschen ( =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted.


title: Bohr model

text: To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing with or with where is constant representing a screening effect due to the inner-shell and other electrons (see Electron shell and the later discussion of the "Shell Model of the Atom" below). This was established empirically before Bohr presented his model.


title: Bohr model

text: Bohr's original three papers in 1913 described mainly the electron configuration in lighter elements. Bohr called his electron shells, “rings” in 1913. Atomic orbitals within shells did not exist at the time of his planetary model. Bohr explains in Part 3 of his famous 1913 paper that the maximum electrons in a shell is eight, writing: “We see, further, that a ring of "n" electrons cannot rotate in a single ring round a nucleus of charge "n" unless "n" < 8.” For smaller atoms, the electron shells would be filled as follows: “rings of electrons will only join together if they contain equal numbers of electrons; and that accordingly the numbers of electrons on inner rings will only be 2, 4, 8”. However, in larger atoms the innermost shell would contain eight electrons, “on the other hand, the periodic system of the elements strongly suggests that already in neon "N" = 10 an inner ring of eight electrons will occur”. Bohr wrote "From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:"


title: Bohr model

text: In Bohr's third 1913 paper Part III called systems containing several nuclei, he says that two atoms form molecules on a symmetrical plane and he reverts to describing Hydrogen. The 1913 Bohr model did not discuss higher elements in detail and John William Nicholson was one of the first to prove in 1914 that it couldn't work for Lithium, but was an attractive theory for Hydrogen and ionized helium.


title: Bohr model

text: In 1921, following the work of chemists and others involved in work on the periodic table, Bohr extended the model of hydrogen to give an approximate model for heavier atoms. This gave a physical picture that reproduced many known atomic properties for the first time although these properties were proposed contemporarily with the identical work of chemist Charles Rugeley Bury


title: Bohr model

text: Bohr's partner in research during 1914 to 1916 was Walther Kossel who corrected Bohr's work to show that electrons interacted through the outer rings, and Kossel called the rings: “shells.” Irving Langmuir is credited with the first viable arrangement of electrons in shells with only two in the first shell and going up to eight in the next according to the octet rule of 1904, although Kossel had already predicted a maximum of eight per shell in 1916. Heavier atoms have more protons in the nucleus, and more electrons to cancel the charge. Bohr took from these chemists the idea that each discrete orbit could only hold a certain number of electrons. Per Kossel, after that the orbit is full, the next level would have to be used. This gives the atom a shell structure designed by Kossel, Langmuir, and Bury, in which each shell corresponds to a Bohr orbit.


title: Bohr model

text: This model is even more approximate than the model of hydrogen, because it treats the electrons in each shell as non-interacting. But the repulsions of electrons are taken into account somewhat by the phenomenon of screening. The electrons in outer orbits do not only orbit the nucleus, but they also move around the inner electrons, so the effective charge Z that they feel is reduced by the number of the electrons in the inner orbit.


title: Bohr model

text: For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at "Z" = 2. Each one sees the nuclear charge of "Z" = 3 minus the screening effect of the other, which crudely reduces the nuclear charge by 1 unit. This means that the innermost electrons orbit at approximately 1/2 the Bohr radius. The outermost electron in lithium orbits at roughly the Bohr radius, since the two inner electrons reduce the nuclear charge by 2. This outer electron should be at nearly one Bohr radius from the nucleus. Because the electrons strongly repel each other, the effective charge description is very approximate; the effective charge "Z" doesn't usually come out to be an integer. But Moseley's law experimentally probes the innermost pair of electrons, and shows that they do see a nuclear charge of approximately "Z" − 1, while the outermost electron in an atom or ion with only one electron in the outermost shell orbits a core with effective charge "Z" − "k" where "k" is the total number of electrons in the inner shells.


title: Bohr model

text: The shell model was able to qualitatively explain many of the mysterious properties of atoms which became codified in the late 19th century in the periodic table of the elements. One property was the size of atoms, which could be determined approximately by measuring the viscosity of gases and density of pure crystalline solids. Atoms tend to get smaller toward the right in the periodic table, and become much larger at the next line of the table. Atoms to the right of the table tend to gain electrons, while atoms to the left tend to lose them. Every element on the last column of the table is chemically inert (noble gas).


title: Bohr model

text: In the shell model, this phenomenon is explained by shell-filling. Successive atoms become smaller because they are filling orbits of the same size, until the orbit is full, at which point the next atom in the table has a loosely bound outer electron, causing it to expand. The first Bohr orbit is filled when it has two electrons, which explains why helium is inert. The second orbit allows eight electrons, and when it is full the atom is neon, again inert. The third orbital contains eight again, except that in the more correct Sommerfeld treatment (reproduced in modern quantum mechanics) there are extra "d" electrons. The third orbit may hold an extra 10 d electrons, but these positions are not filled until a few more orbitals from the next level are filled (filling the n=3 d orbitals produces the 10 transition elements). The irregular filling pattern is an effect of interactions between electrons, which are not taken into account in either the Bohr or Sommerfeld models and which are difficult to calculate even in the modern treatment.


title: Bohr model

text: Niels Bohr said in 1962: "You see actually the Rutherford work was not taken seriously. We cannot understand today, but it was not taken seriously at all. There was no mention of it any place. The great change came from Moseley."


title: Bohr model

text: In 1913, Henry Moseley found an empirical relationship between the strongest X-ray line emitted by atoms under electron bombardment (then known as the K-alpha line), and their atomic number . Moseley's empiric formula was found to be derivable from Rydberg's formula and later Bohr's formula (Moseley actually mentions only Ernest Rutherford and Antonius Van den Broek in terms of models as these had been published before Moseley's work and Moseley's 1913 paper was published the same month as the first Bohr model paper). The two additional assumptions that [1] this X-ray line came from a transition between energy levels with quantum numbers 1 and 2, and [2], that the atomic number when used in the formula for atoms heavier than hydrogen, should be diminished by 1, to .


title: Bohr model

text: Moseley wrote to Bohr, puzzled about his results, but Bohr was not able to help. At that time, he thought that the postulated innermost "K" shell of electrons should have at least four electrons, not the two which would have neatly explained the result. So Moseley published his results without a theoretical explanation.


title: Bohr model

text: It was Walther Kossel in 1914 and in 1916 who explained that in the periodic table new elements would be created as electrons were added to the outer shell. In Kossel's paper, he writes: “This leads to the conclusion that the electrons, which are added further, should be put into concentric rings or shells, on each of which ... only a certain number of electrons—namely, eight in our case—should be arranged. As soon as one ring or shell is completed, a new one has to be started for the next element; the number of electrons, which are most easily accessible, and lie at the outermost periphery, increases again from element to element and, therefore, in the formation of each new shell the chemical periodicity is repeated.” Later, chemist Langmuir realized that the effect was caused by charge screening, with an inner shell containing only 2 electrons. In his 1919 paper, Irving Langmuir postulated the existence of "cells" which could each only contain two electrons each, and these were arranged in "equidistant layers”.


title: Bohr model

text: In the Moseley experiment, one of the innermost electrons in the atom is knocked out, leaving a vacancy in the lowest Bohr orbit, which contains a single remaining electron. This vacancy is then filled by an electron from the next orbit, which has n=2. But the n=2 electrons see an effective charge of "Z" − 1, which is the value appropriate for the charge of the nucleus, when a single electron remains in the lowest Bohr orbit to screen the nuclear charge +"Z", and lower it by −1 (due to the electron's negative charge screening the nuclear positive charge). The energy gained by an electron dropping from the second shell to the first gives Moseley's law for K-alpha lines,


title: Bohr model

text: Here, R" = R"/"h" is the Rydberg constant, in terms of frequency equal to 3.28 x 10 Hz. For values of Z between 11 and 31 this latter relationship had been empirically derived by Moseley, in a simple (linear) plot of the square root of X-ray frequency against atomic number (however, for silver, Z = 47, the experimentally obtained screening term should be replaced by 0.4). Notwithstanding its restricted validity, Moseley's law not only established the objective meaning of atomic number, but as Bohr noted, it also did more than the Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge. Van den Broek had published his model in January 1913 showing the periodic table was arranged according to charge while Bohr's atomic model was not published until July 1913.


title: Bohr model

text: The K-alpha line of Moseley's time is now known to be a pair of close lines, written as (Kα and Kα) in Siegbahn notation.


title: Bohr model

text: The Bohr model gives an incorrect value for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to rotate "around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus). This is only reproduced in a more sophisticated semiclassical treatment like Sommerfeld's. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric – it doesn't point in any particular direction.


title: Bohr model

text: Nevertheless, in the modern "fully quantum treatment in phase space", the proper deformation (careful full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. As a consequence, the physical ground state expression is obtained through a shift of the vanishing quantum angular momentum expression, which corresponds to spherical symmetry.


title: Bohr model

text: In modern quantum mechanics, the electron in hydrogen is a spherical cloud of probability that grows denser near the nucleus. The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a "coincidence". (However, many such coincidental agreements are found between the semiclassical vs. full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine-structure constant, which arises from the relativistic Bohr–Sommerfeld model (see below) and which happens to be equal to an entirely different concept, in full modern quantum mechanics).


title: Bohr model

text: Several enhancements to the Bohr model were proposed, most notably the Sommerfeld or Bohr–Sommerfeld models, which suggested that electrons travel in elliptical orbits around a nucleus instead of the Bohr model's circular orbits. This model supplemented the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition


title: Bohr model

text: where "p" is the radial momentum canonically conjugate to the coordinate "q", which is the radial position, and "T" is one full orbital period. The integral is the action of action-angle coordinates. This condition, suggested by the correspondence principle, is the only one possible, since the quantum numbers are adiabatic invariants.


title: Bohr model

text: The Bohr–Sommerfeld model was fundamentally inconsistent and led to many paradoxes. The magnetic quantum number measured the tilt of the orbital plane relative to the "xy" plane, and it could only take a few discrete values. This contradicted the obvious fact that an atom could be turned this way and that relative to the coordinates without restriction. The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers. The incorporation of radiation corrections was difficult, because it required finding action-angle coordinates for a combined radiation/atom system, which is difficult when the radiation is allowed to escape. The whole theory did not extend to non-integrable motions, which meant that many systems could not be treated even in principle. In the end, the model was replaced by the modern quantum-mechanical treatment of the hydrogen atom, which was first given by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics. The current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics, which Erwin Schrödinger developed in 1926.


title: Bohr model

text: However, this is not to say that the Bohr–Sommerfeld model was without its successes. Calculations based on the Bohr–Sommerfeld model were able to accurately explain a number of more complex atomic spectral effects. For example, up to first-order perturbations, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and measurements of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model. The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary according to the energy state of the electron.


title: Bohr model

text: The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics. Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized. In particular, the symplectic form should be the curvature form of a connection of a Hermitian line bundle, which is called a prequantization.


title: Bohr model

text: Bohr also updated his model in 1922, assuming that certain numbers of electrons (for example, 2, 8, and 18) correspond to stable "closed shells".


title: Bohr model

text: Niels Bohr proposed a model of the atom and a model of the chemical bond. According to his model for a diatomic molecule, the electrons of the atoms of the molecule form a rotating ring whose plane is perpendicular to the axis of the molecule and equidistant from the atomic nuclei. The dynamic equilibrium of the molecular system is achieved through the balance of forces between the forces of attraction of nuclei to the plane of the ring of electrons and the forces of mutual repulsion of the nuclei. The Bohr model of the chemical bond took into account the Coulomb repulsion – the electrons in the ring are at the maximum distance from each other.


title: Compound interest

text: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.


title: Compound interest

text: Compound interest is contrasted with "simple interest", where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The "simple annual interest rate" is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).


title: Compound interest

text: The "compounding frequency" is the number of times per year (or rarely, another unit of time) the accumulated interest is paid out, or "capitalized" (credited to the account), on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, or continuously (or not at all, until maturity).


title: Compound interest

text: For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months.


title: Compound interest

text: The nominal rate cannot be directly compared between loans with different compounding frequencies. Both the nominal interest rate and the compounding frequency are required in order to compare interest-bearing financial instruments.


title: Compound interest

text: To help consumers compare retail financial products more fairly and easily, many countries require financial institutions to disclose the annual compound interest rate on deposits or advances on a comparable basis. The interest rate on an annual equivalent basis may be referred to variously in different markets as effective "annual percentage rate" (EAPR), "annual equivalent rate" (AER), "effective interest rate", "effective annual rate", "annual percentage yield" and other terms. The effective annual rate is the total accumulated interest that would be payable up to the end of one year, divided by the principal sum.


title: Compound interest

text: The total accumulated value, including the principal sum formula_1 plus compounded interest formula_2, is given by the formula:


title: Compound interest

text: Suppose a principal amount of $1,500 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly.<br> Then the balance after 6 years is found by using the formula above, with "P" = 1500, "r" = 0.043 (4.3%), "n" = 4, and "t" = 6:


title: Compound interest

text: Suppose the same amount of $1,500 is compounded biennially (every 2 years). (This is very unusual in practice.) Then the balance after 6 years is found by using the formula above, with "P" = 1500, "r" = 0.043 (4.3%), "n" = 1/2 (the interest is compounded every two years), and "t" = 6 :


title: Compound interest

text: The interest is less compared with the previous case, as a result of the lower compounding frequency.


title: Compound interest

text: Since the principal "P" is simply a coefficient, it is often dropped for simplicity, and the resulting accumulation function is used instead. The accumulation function shows what $1 grows to after any length of time.


title: Compound interest

text: As "n", the number of compounding periods per year, increases without limit, the case is known as continuous compounding, in which case the effective annual rate approaches an upper limit of , where is a mathematical constant that is the base of the natural logarithm.


title: Compound interest

text: Continuous compounding can be thought of as making the compounding period infinitesimally small, achieved by taking the limit as "n" goes to infinity. See definitions of the exponential function for the mathematical proof of this limit. The amount after "t" periods of continuous compounding can be expressed in terms of the initial amount "P" as


title: Compound interest

text: As the number of compounding periods formula_13 tends to infinity in continuous compounding, the continuous compound interest rate is referred to as the force of interest formula_14.


title: Compound interest

text: In mathematics, the accumulation functions are often expressed in terms of "e", the base of the natural logarithm. This facilitates the use of calculus to manipulate interest formulae.


title: Compound interest

text: For any continuously differentiable accumulation function "a"("t"), the force of interest, or more generally the logarithmic or continuously compounded return is a function of time defined as follows:


title: Compound interest

text: When the above formula is written in differential equation format, then the force of interest is simply the coefficient of amount of change:


title: Compound interest

text: For compound interest with a constant annual interest rate "r", the force of interest is a constant, and the accumulation function of compounding interest in terms of force of interest is a simple power of "e":


title: Compound interest

text: The force of interest is less than the annual effective interest rate, but more than the annual effective discount rate. It is the reciprocal of the "e"-folding time. See also notation of interest rates.


title: Compound interest

text: A way of modeling the force of inflation is with Stoodley's formula: formula_21 where "p", "r" and "s" are estimated.


title: Compound interest

text: The interest on loans and mortgages that are amortized—that is, have a smooth monthly payment until the loan has been paid off—is often compounded monthly. The formula for payments is found from the following argument.


title: Compound interest

text: This can be derived by considering how much is left to be repaid after each month. <br>The Principal remaining after the first month is


title: Compound interest

text: that is, the initial amount plus interest less the payment. <br>If the whole loan is repaid after one month then


title: Compound interest

text: This equation generalises for a term of "n" months, formula_39. This is a geometric series which has the sum


title: Compound interest

text: For example, for interest rate of 6% (0.06/12), 25 years * 12 p.a., PV of $150,000, FV of 0, type of 0 gives:


title: Compound interest

text: noting that for typical U.S. note rates (formula_42 and terms formula_43=10–30 years), the monthly note rate is small compared to 1:


title: Compound interest

text: Here formula_49 is the monthly payment required for a zero–interest loan paid off in formula_13 installments. In terms of these variables the approximation can be written


title: Compound interest

text: It follows immediately that formula_55 can be expanded in even powers of formula_54 plus the single term: formula_57


title: Compound interest

text: The exact payment amount is formula_68 so the approximation is an overestimate of about a sixth of a percent.


title: Compound interest

text: Given an principal (initial) deposit and a recurring deposit, the total return of an investment can be calculated via the compound interest gained per unit of time. If required, the interest on additional non-recurring and recurring deposits can also be defined within the same formula (see below).


title: Compound interest

text: and adding all recurring deposits over the total period t (i starts at 0 if deposits begin with the investment of principal; i starts at 1 if deposits begin the next month) :


title: Compound interest

text: recognizing the geometric series: formula_75 and applying the closed-form formula (common ratio :formula_76) we obtain:


title: Compound interest

text: If two or more types of deposits occur (either recurring or non-recurring), the compound value earned can be represented as


title: Compound interest

text: where C is each lump sum and k are non-monthly recurring deposits, respectively, and x and y are the differences in time between a new deposit and the total period t is modeling.


title: Compound interest

text: A practical estimate for reverse calculation of the rate of return when the exact date and amount of each recurring deposit is not known, a formula that assumes a uniform recurring monthly deposit over the period, is:


title: Compound interest

text: Compound interest when charged by lenders was once regarded as the worst kind of usury and was severely condemned by Roman law and the common laws of many other countries.


title: Compound interest

text: The Florentine merchant Francesco Balducci Pegolotti provided a table of compound interest in his book "Pratica della mercatura" of about 1340. It gives the interest on 100 lire, for rates from 1% to 8%, for up to 20 years. The "Summa de arithmetica" of Luca Pacioli (1494) gives the Rule of 72, stating that to find the number of years for an investment at compound interest to double, one should divide the interest rate into 72.


title: Compound interest

text: Richard Witt's book "Arithmeticall Questions", published in 1613, was a landmark in the history of compound interest. It was wholly devoted to the subject (previously called anatocism), whereas previous writers had usually treated compound interest briefly in just one chapter in a mathematical textbook. Witt's book gave tables based on 10% (the then maximum rate of interest allowable on loans) and on other rates for different purposes, such as the valuation of property leases. Witt was a London mathematical practitioner and his book is notable for its clarity of expression, depth of insight and accuracy of calculation, with 124 worked examples.


title: Compound interest

text: Jacob Bernoulli discovered the constant formula_81 in 1683 by studying a question about compound interest.


title: Compound interest

text: In the 19th century, and possibly earlier, Persian merchants used a slightly modified linear Taylor approximation to the monthly payment formula that could be computed easily in their heads.


title: Apathy

text: Apathy is a lack of feeling, emotion, interest, or concern about something. It is a state of indifference, or the suppression of emotions such as concern, excitement, motivation, or passion. An apathetic individual has an absence of interest in or concern about emotional, social, spiritual, philosophical, virtual, or physical life and the world. Apathy can also be defined as a person's lack of goal orientation. Apathy falls in the less extreme spectrum of diminished motivation, with abulia in the middle and akinetic mutism being more extreme than both apathy and abulia.


title: Apathy

text: The apathetic may lack a sense of purpose, worth, or meaning in their life. People with severe apathy tend to have a lower quality of life and are at a higher risk for mortality and early institutionalization. They may also exhibit insensibility or sluggishness. In positive psychology, apathy is described as a result of the individuals' feeling they do not possess the level of skill required to confront a challenge (i.e. "flow"). It may also be a result of perceiving no challenge at all (e.g. the challenge is irrelevant to them, or conversely, they have learned helplessness). Apathy is something that all people face in some capacity and is a natural response to disappointment, dejection, and stress. As a response, apathy is a way to forget about these negative feelings. This type of common apathy is usually felt only in the short term, but sometimes it becomes a long-term or even lifelong state, often leading to deeper social and psychological issues. An extreme form of apathy may be someone being numb to different stressful life events such as losing a job.


title: Apathy

text: Apathy should be distinguished from reduced affect display, which refers to reduced emotional expression but not necessarily reduced emotion.


title: Apathy

text: Pathological apathy, characterized by extreme forms of apathy, is now known to occur in many different brain disorders, including neurodegenerative conditions often associated with dementia such as Alzheimer's disease, Parkinson's disease, and psychiatric disorders such as schizophrenia. Although many patients with pathological apathy also have depression, several studies have shown that the two syndromes are dissociable: apathy can occur independently of depression and vice versa.


title: Apathy

text: Although the word "apathy" was first used in 1594 and is derived from the Greek ("apatheia"), from ("apathēs", "without feeling" from "a-" ("without, not") and "pathos" ("emotion")), it is important not to confuse the two terms. Also meaning "absence of passion," "apathy" or "insensibility" in Greek, the term "apatheia" was used by the Stoics to signify a (desirable) state of indifference towards events and things which lie outside one's control (that is, according to their philosophy, all things exterior, one being only responsible for one's own representations and judgments). In contrast to "apathy", "apatheia" is considered a virtue, especially in Orthodox monasticism. In the Philokalia the word "dispassion" is used for "apatheia", so as not to confuse it with "apathy".


title: Apathy

text: Christians have historically condemned apathy as a deficiency of love and devotion to God and his works. This interpretation of apathy is also referred to as Sloth and is listed among the Seven Deadly Sins. Clemens Alexandrinus used the term to draw to Christianity philosophers who aspired after virtue.