| [ | |
| { | |
| "problem_text": "Calculate the de Broglie wavelength for an electron with a kinetic energy of $100 \\mathrm{eV}$", | |
| "answer_latex": " 0.123", | |
| "answer_number": "0.123", | |
| "unit": "nm ", | |
| "source": "chemmc", | |
| "problemid": "1-38 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "The threshold wavelength for potassium metal is $564 \\mathrm{~nm}$. What is its work function? \r\n", | |
| "answer_latex": " 3.52", | |
| "answer_number": "3.52", | |
| "unit": "$10^{-19} \\mathrm{~J}$", | |
| "source": "chemmc", | |
| "problemid": " 1-18", | |
| "comment": " Only the first part, the work function is taken" | |
| }, | |
| { | |
| "problem_text": "Evaluate the series\r\n$$\r\nS=\\sum_{n=0}^{\\infty} \\frac{1}{3^n}\r\n$$", | |
| "answer_latex": " 3 / 2", | |
| "answer_number": "1.5", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": "D-7 ", | |
| "comment": " Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "The relationship introduced in Problem $1-48$ has been interpreted to mean that a particle of mass $m\\left(E=m c^2\\right)$ can materialize from nothing provided that it returns to nothing within a time $\\Delta t \\leq h / m c^2$. Particles that last for time $\\Delta t$ or more are called real particles; particles that last less than time $\\Delta t$ are called virtual particles. The mass of the charged pion, a subatomic particle, is $2.5 \\times 10^{-28} \\mathrm{~kg}$. What is the minimum lifetime if the pion is to be considered a real particle?", | |
| "answer_latex": " 2.9", | |
| "answer_number": "2.9", | |
| "unit": "$10^{-23} \\mathrm{~s}$ ", | |
| "source": "chemmc", | |
| "problemid": "1-49 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "A household lightbulb is a blackbody radiator. Many lightbulbs use tungsten filaments that are heated by an electric current. What temperature is needed so that $\\lambda_{\\max }=550 \\mathrm{~nm}$ ?", | |
| "answer_latex": " 5300", | |
| "answer_number": "5300", | |
| "unit": " $\\mathrm{~K}$\r\n", | |
| "source": "chemmc", | |
| "problemid": " 1-17", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Evaluate the series\r\n$$\r\nS=\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{16}+\\cdots\r\n$$\r\n", | |
| "answer_latex": " 1", | |
| "answer_number": "1", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": " D-6", | |
| "comment": " Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "Through what potential must a proton initially at rest fall so that its de Broglie wavelength is $1.0 \\times 10^{-10} \\mathrm{~m}$ ?", | |
| "answer_latex": " 0.082", | |
| "answer_number": "0.082", | |
| "unit": "V ", | |
| "source": "chemmc", | |
| "problemid": "1-40 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Example 5-3 shows that a Maclaurin expansion of a Morse potential leads to\r\n$$\r\nV(x)=D \\beta^2 x^2+\\cdots\r\n$$\r\nGiven that $D=7.31 \\times 10^{-19} \\mathrm{~J} \\cdot$ molecule ${ }^{-1}$ and $\\beta=1.81 \\times 10^{10} \\mathrm{~m}^{-1}$ for $\\mathrm{HCl}$, calculate the force constant of $\\mathrm{HCl}$.", | |
| "answer_latex": " 479", | |
| "answer_number": "479", | |
| "unit": "$\\mathrm{~N} \\cdot \\mathrm{m}^{-1}$ ", | |
| "source": "chemmc", | |
| "problemid": "5-9 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "A line in the Lyman series of hydrogen has a wavelength of $1.03 \\times 10^{-7} \\mathrm{~m}$. Find the original energy level of the electron.", | |
| "answer_latex": " 3", | |
| "answer_number": "3", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": " 1-25", | |
| "comment": " no units" | |
| }, | |
| { | |
| "problem_text": "A helium-neon laser (used in supermarket scanners) emits light at $632.8 \\mathrm{~nm}$. Calculate the frequency of this light.", | |
| "answer_latex": " 4.738", | |
| "answer_number": "4.738", | |
| "unit": "$10^{14} \\mathrm{~Hz}$ ", | |
| "source": "chemmc", | |
| "problemid": " 1-15", | |
| "comment": " just the first part is taken: frequency of light" | |
| }, | |
| { | |
| "problem_text": "What is the uncertainty of the momentum of an electron if we know its position is somewhere in a $10 \\mathrm{pm}$ interval?", | |
| "answer_latex": " 6.6", | |
| "answer_number": " 6.6", | |
| "unit": " $10^{-23} \\mathrm{~kg} \\cdot \\mathrm{m} \\cdot \\mathrm{s}^{-1}$", | |
| "source": "chemmc", | |
| "problemid": "1-47 ", | |
| "comment": " discard the second part of the answer" | |
| }, | |
| { | |
| "problem_text": "Using the Bohr theory, calculate the ionization energy (in electron volts and in $\\mathrm{kJ} \\cdot \\mathrm{mol}^{-1}$ ) of singly ionized helium.", | |
| "answer_latex": " 54.394", | |
| "answer_number": "54.394", | |
| "unit": "$\\mathrm{eV}$ ", | |
| "source": "chemmc", | |
| "problemid": "1-34 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "When an excited nucleus decays, it emits a $\\gamma$ ray. The lifetime of an excited state of a nucleus is of the order of $10^{-12} \\mathrm{~s}$. What is the uncertainty in the energy of the $\\gamma$ ray produced?", | |
| "answer_latex": " 7", | |
| "answer_number": "7", | |
| "unit": "$10^{-22} \\mathrm{~J}$ ", | |
| "source": "chemmc", | |
| "problemid": "1-51 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Calculate the wavelength and the energy of a photon associated with the series limit of the Lyman series.", | |
| "answer_latex": " 91.17", | |
| "answer_number": "91.17", | |
| "unit": "nm ", | |
| "source": "chemmc", | |
| "problemid": " 1-28", | |
| "comment": "only the first part of the question, the wavelength" | |
| }, | |
| { | |
| "problem_text": "Given a context information that there is also an uncertainty principle for energy and time:\n$$\n\\Delta E \\Delta t \\geq h\n$$, another application of the relationship has to do with the excitedstate energies and lifetimes of atoms and molecules. If we know that the lifetime of an excited state is $10^{-9} \\mathrm{~s}$, then what is the uncertainty in the energy of this state?", | |
| "answer_latex": " 7", | |
| "answer_number": "7", | |
| "unit": " $10^{-25} \\mathrm{~J}$", | |
| "source": "chemmc", | |
| "problemid": " 1-50", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "One of the most powerful modern techniques for studying structure is neutron diffraction. This technique involves generating a collimated beam of neutrons at a particular temperature from a high-energy neutron source and is accomplished at several accelerator facilities around the world. If the speed of a neutron is given by $v_{\\mathrm{n}}=\\left(3 k_{\\mathrm{B}} T / m\\right)^{1 / 2}$, where $m$ is the mass of a neutron, then what temperature is needed so that the neutrons have a de Broglie wavelength of $50 \\mathrm{pm}$ ?", | |
| "answer_latex": " 2500", | |
| "answer_number": "2500", | |
| "unit": "$\\mathrm{K}$ ", | |
| "source": "chemmc", | |
| "problemid": "1-42 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "The temperature of the fireball in a thermonuclear explosion can reach temperatures of approximately $10^7 \\mathrm{~K}$. What value of $\\lambda_{\\max }$ does this correspond to? ", | |
| "answer_latex": " 3", | |
| "answer_number": "3", | |
| "unit": " $10^{-10} \\mathrm{~m}$\r\n", | |
| "source": "chemmc", | |
| "problemid": "1-8 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Show that l'H\u00f4pital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit\r\n$$\r\n\\lim _{x \\rightarrow 0} \\frac{\\ln (1+x)-x}{x^2}\r\n$$\r\nboth ways and report the final result.", | |
| "answer_latex": " -1/2", | |
| "answer_number": "-0.5", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": "D-21 ", | |
| "comment": " Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "Evaluate the series\r\n$$\r\nS=\\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{2^n}\r\n$$", | |
| "answer_latex": " 1/3", | |
| "answer_number": "0.3333333", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": " D-8", | |
| "comment": " Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "Calculate the percentage difference between $\\ln (1+x)$ and $x$ for $x=0.0050$", | |
| "answer_latex": " 0.249", | |
| "answer_number": "0.249", | |
| "unit": " %", | |
| "source": "chemmc", | |
| "problemid": " D-4", | |
| "comment": " Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "Calculate the reduced mass of a nitrogen molecule in which both nitrogen atoms have an atomic mass of 14.00.", | |
| "answer_latex": " 7.00", | |
| "answer_number": "7.00", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": "1-30 ", | |
| "comment": "no units " | |
| }, | |
| { | |
| "problem_text": "Two narrow slits are illuminated with red light of wavelength $694.3 \\mathrm{~nm}$ from a laser, producing a set of evenly placed bright bands on a screen located $3.00 \\mathrm{~m}$ beyond the slits. If the distance between the bands is $1.50 \\mathrm{~cm}$, then what is the distance between the slits?\r\n", | |
| "answer_latex": " 0.139", | |
| "answer_number": "0.139", | |
| "unit": "mm ", | |
| "source": "chemmc", | |
| "problemid": "1-45 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Calculate the energy associated with an $\\alpha$ particle that has fallen through a potential difference of $4.0 \\mathrm{~V}$. Take the mass of an $\\alpha$ particle to be $6.64 \\times 10^{-27} \\mathrm{~kg}$.", | |
| "answer_latex": " 1.3", | |
| "answer_number": "1.3", | |
| "unit": "$10^{-18} \\mathrm{~J} / \\alpha \\text {-particle}$", | |
| "source": "chemmc", | |
| "problemid": "1-41 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Calculate the number of photons in a $2.00 \\mathrm{~mJ}$ light pulse at (a) $1.06 \\mu \\mathrm{m}$\r\n", | |
| "answer_latex": " 1.07", | |
| "answer_number": "1.07", | |
| "unit": " $10^{16}$ photons", | |
| "source": "chemmc", | |
| "problemid": " 1-13", | |
| "comment": " part (a) only" | |
| }, | |
| { | |
| "problem_text": "The force constant of ${ }^{35} \\mathrm{Cl}^{35} \\mathrm{Cl}$ is $319 \\mathrm{~N} \\cdot \\mathrm{m}^{-1}$. Calculate the fundamental vibrational frequency", | |
| "answer_latex": " 556", | |
| "answer_number": "556", | |
| "unit": " $\\mathrm{~cm}^{-1}$", | |
| "source": "chemmc", | |
| "problemid": " 5-14", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "$$\r\n\\text {Calculate the energy of a photon for a wavelength of } 100 \\mathrm{pm} \\text { (about one atomic diameter). }\r\n$$\r\n", | |
| "answer_latex": " 2", | |
| "answer_number": "2", | |
| "unit": " $10^{-15} \\mathrm{~J}$", | |
| "source": "chemmc", | |
| "problemid": "1-11 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "A proton and a negatively charged $\\mu$ meson (called a muon) can form a short-lived species called a mesonic atom. The charge of a muon is the same as that on an electron and the mass of a muon is $207 m_{\\mathrm{e}}$. Assume that the Bohr theory can be applied to such a mesonic atom and calculate the frequency associated with the $n=1$ to $n=2$ transition in a mesonic atom.", | |
| "answer_latex": " 1.69", | |
| "answer_number": "4.59", | |
| "unit": "$10^{17} \\mathrm{~Hz}$", | |
| "source": "chemmc", | |
| "problemid": " 1-37", | |
| "comment": " only the ground state energy is there" | |
| }, | |
| { | |
| "problem_text": "$$\r\n\\beta=2 \\pi c \\tilde{\\omega}_{\\mathrm{obs}}\\left(\\frac{\\mu}{2 D}\\right)^{1 / 2}\r\n$$\r\nGiven that $\\tilde{\\omega}_{\\mathrm{obs}}=2886 \\mathrm{~cm}^{-1}$ and $D=440.2 \\mathrm{~kJ} \\cdot \\mathrm{mol}^{-1}$ for $\\mathrm{H}^{35} \\mathrm{Cl}$, calculate $\\beta$.", | |
| "answer_latex": " 1.81", | |
| "answer_number": "1.81", | |
| "unit": " $10^{10} \\mathrm{~m}^{-1}$", | |
| "source": "chemmc", | |
| "problemid": " 5-10", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Two narrow slits separated by $0.10 \\mathrm{~mm}$ are illuminated by light of wavelength $600 \\mathrm{~nm}$. If a detector is located $2.00 \\mathrm{~m}$ beyond the slits, what is the distance between the central maximum and the first maximum?", | |
| "answer_latex": " 12", | |
| "answer_number": "12", | |
| "unit": " mm", | |
| "source": "chemmc", | |
| "problemid": "1-44 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "$$\r\n\\text { If we locate an electron to within } 20 \\mathrm{pm} \\text {, then what is the uncertainty in its speed? }\r\n$$", | |
| "answer_latex": " 3.7", | |
| "answer_number": "3.7", | |
| "unit": "$10^7 \\mathrm{~m} \\cdot \\mathrm{s}^{-1}$ ", | |
| "source": "chemmc", | |
| "problemid": "1-46 ", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "The mean temperature of the earth's surface is $288 \\mathrm{~K}$. What is the maximum wavelength of the earth's blackbody radiation?", | |
| "answer_latex": " 1.01", | |
| "answer_number": "1.01", | |
| "unit": " 10^{-5} \\mathrm{~m}", | |
| "source": "chemmc", | |
| "problemid": " 1-14", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "The power output of a laser is measured in units of watts (W), where one watt is equal to one joule per second. $\\left(1 \\mathrm{~W}=1 \\mathrm{~J} \\cdot \\mathrm{s}^{-1}\\right.$.) What is the number of photons emitted per second by a $1.00 \\mathrm{~mW}$ nitrogen laser? The wavelength emitted by a nitrogen laser is $337 \\mathrm{~nm}$.", | |
| "answer_latex": " 1.70", | |
| "answer_number": "1.70", | |
| "unit": " $\r\n10^{15} \\text { photon } \\cdot \\mathrm{s}^{-1}\r\n$", | |
| "source": "chemmc", | |
| "problemid": " 1-16", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": " Sirius, one of the hottest known stars, has approximately a blackbody spectrum with $\\lambda_{\\max }=260 \\mathrm{~nm}$. Estimate the surface temperature of Sirius.\r\n", | |
| "answer_latex": "11000", | |
| "answer_number": "11000", | |
| "unit": " $\\mathrm{~K}$\r\n", | |
| "source": "chemmc", | |
| "problemid": " 1-7", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "A ground-state hydrogen atom absorbs a photon of light that has a wavelength of $97.2 \\mathrm{~nm}$. It then gives off a photon that has a wavelength of $486 \\mathrm{~nm}$. What is the final state of the hydrogen atom?", | |
| "answer_latex": " 2", | |
| "answer_number": "2", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": " 1-26", | |
| "comment": " no units" | |
| }, | |
| { | |
| "problem_text": "It turns out that the solution of the Schr\u00f6dinger equation for the Morse potential can be expressed as\r\n$$\r\nG(v)=\\tilde{\\omega}_{\\mathrm{e}}\\left(v+\\frac{1}{2}\\right)-\\tilde{\\omega}_{\\mathrm{e}} \\tilde{x}_{\\mathrm{e}}\\left(v+\\frac{1}{2}\\right)^2\r\n$$\r\nThe Harmonic Oscillator and Vibrational Spectroscopy\r\nwhere\r\n$$\r\n\\tilde{x}_{\\mathrm{e}}=\\frac{h c \\tilde{\\omega}_{\\mathrm{e}}}{4 D}\r\n$$\r\nGiven that $\\tilde{\\omega}_{\\mathrm{e}}=2886 \\mathrm{~cm}^{-1}$ and $D=440.2 \\mathrm{~kJ} \\cdot \\mathrm{mol}^{-1}$ for $\\mathrm{H}^{35} \\mathrm{Cl}$, calculate $\\tilde{x}_{\\mathrm{e}}$.", | |
| "answer_latex": " 0.01961", | |
| "answer_number": " 0.01961", | |
| "unit": " ", | |
| "source": "chemmc", | |
| "problemid": "5-12 ", | |
| "comment": "only first part taken of the question " | |
| }, | |
| { | |
| "problem_text": " In the infrared spectrum of $\\mathrm{H}^{127} \\mathrm{I}$, there is an intense line at $2309 \\mathrm{~cm}^{-1}$. Calculate the force constant of $\\mathrm{H}^{127} \\mathrm{I}$.", | |
| "answer_latex": "313", | |
| "answer_number": "313", | |
| "unit": " $ \\mathrm{~N} \\cdot \\mathrm{m}^{-1}$", | |
| "source": "chemmc", | |
| "problemid": " 5-13", | |
| "comment": " " | |
| }, | |
| { | |
| "problem_text": "Calculate the percentage difference between $e^x$ and $1+x$ for $x=0.0050$", | |
| "answer_latex": " 1.25", | |
| "answer_number": "1.25", | |
| "unit": " $10^{-3} \\%$", | |
| "source": "chemmc", | |
| "problemid": "D-1", | |
| "comment": "Math Part D (after chapter 4)" | |
| }, | |
| { | |
| "problem_text": "Calculate the kinetic energy of an electron in a beam of electrons accelerated by a voltage increment of $100 \\mathrm{~V}$", | |
| "answer_latex": " 1.602", | |
| "answer_number": "1.602", | |
| "unit": " $10^{-17} \\mathrm{~J} \\cdot$ electron ${ }^{-1}$", | |
| "source": "chemmc", | |
| "problemid": "1-39 ", | |
| "comment": " " | |
| } | |
| ] |