Electron shell

In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the " shell" (also called the "K shell"), followed by the " shell" (or "L shell"), then the " shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond to the principal quantum numbers ("n" = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, …).
Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the "n"th shell can in principle hold up to 2("n"2) electrons. For an explanation of why electrons exist in these shells see electron configuration.
Each shell consists of one or more "subshells", and each subshell consists of one or more atomic orbitals.
History.
The shell terminology comes from Arnold Sommerfeld's modification of the Bohr model. Sommerfeld retained Bohr's planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers "" and "m") to explain the fine spectroscopic structure of some elements. The multiple electrons with the same principal quantum number ("n") had close orbits that formed a "shell" of positive thickness instead of the infinitely thin circular orbit of Bohr's model.
The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies. Barkla labeled them with the letters K, L, M, N, O, P, and Q. The origin of this terminology was alphabetic. A "J" series was also suspected, though later experiments indicated that the K absorption lines are produced by the innermost electrons. These letters were later found to correspond to the "n" values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation.
Subshells.
Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called ; the second (L) shell has two subshells, called and ; the third shell has , , and ; the fourth shell has , , and ; the fifth shell has , , , and and can theoretically hold more in the subshell that is not occupied in the ground-state electron configuration of any known element. The various possible subshells are shown in the following table:
Number of electrons in each shell.
Each subshell is constrained to hold electrons at most, namely:
Therefore, the K shell, which contains only an subshell, can hold up to 2 electrons; the L shell, which contains an and a , can hold up to 2 + 6 = 8 electrons, and so forth; in general, the "n"th shell can hold up to 2"n"2 electrons.
Although that formula gives the maximum in principle, in fact that maximum is only "achieved" (by known elements) for the first four shells (K, L, M, N). No known element has more than 32 electrons in any one shell. This is because the subshells are filled according to the Aufbau principle. The first elements to have more than 32 electrons in one shell would belong to the g-block of period 8 of the periodic table. These elements would have some electrons in their subshell and thus have more than 32 electrons in the O shell (fifth principal shell).
Subshell energies and filling order.
Although it is sometimes stated that all the electrons in a shell have the same energy, this is an approximation. However, the electrons in one "subshell" do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This effect is great enough that the energy ranges associated with shells can overlap.
The filling of the shells and subshells with electrons proceeds from subshells of lower energy to subshells of higher energy. This follows the "n + ℓ rule" which is also commonly known as the Madelung rule. Subshells with a lower "n + ℓ" value are filled before those with higher "n + ℓ" values. In the case of equal "n + ℓ" values, the subshell with a lower "n" value is filled first.
List of elements with electrons per shell.
The list below gives the elements arranged by increasing atomic number and shows the number of electrons per shell. At a glance, the subsets of the list show obvious patterns. In particular, every set of five elements (in ) before each noble gas (group 18, in ) heavier than helium have successive numbers of electrons in the outermost shell, namely three to seven.
Sorting the table by chemical group shows additional patterns, especially with respect to the last two outermost shells. (Elements 57 to 71 belong to the lanthanides, while 89 to 103 are the actinides.)
The list below is primarily consistent with the Aufbau principle. However, there are a number of exceptions to the rule; for example palladium (atomic number 46) has no electrons in the fifth shell, unlike other atoms with "lower" atomic number. Some entries in the table are uncertain, when experimental data is unavailable. (For example, the elements past 108 have such short half-lives that their electron configurations have not yet been measured.)