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This notation is used to specify electron configurations and to create the term symbol for the electron states in a multi-electron atom. When writing a term symbol, the above scheme for a single electron's orbital quantum number is applied to the total orbital angular momentum associated to an electron state. [4]
# is an additional number denoted to each energy level of given n′ℓ (there can be multiple energy levels of given electronic configuration, denoted by the term symbol). # denotes each level in order, for example, # = 10 is for a lower energy level than # = 9 level and # = 1 is for the highest level in a given n′ℓ .
As an example, consider the ground state of silicon.The electron configuration of Si is 1s 2 2s 2 2p 6 3s 2 3p 2 (see spectroscopic notation).We need to consider only the outer 3p 2 electrons, for which it can be shown (see term symbols) that the possible terms allowed by the Pauli exclusion principle are 1 D , 3 P , and 1 S.
Configurations of elements 109 and above are not available. Predictions from reliable sources have been used for these elements. Grayed out electron numbers indicate subshells filled to their maximum. Bracketed noble gas symbols on the left represent inner configurations that are the same in each period. Written out, these are: He, 2, helium : 1s 2
Term symbols (e.g. 3 P, 1 S, etc.) for a specific d n free ion are listed, in order of increasing energy, on the y-axis of the diagram. The relative order of energies is determined using Hund's rules. For an octahedral complex, the spherical, free ion term symbols split accordingly: [9]
However there are numerous exceptions; for example the lightest exception is chromium, which would be predicted to have the configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 4 4s 2, written as [Ar] 3d 4 4s 2, but whose actual configuration given in the table below is [Ar] 3d 5 4s 1.
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Lithium has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s 2 2s 1 (pronounced "one-s-two, two-s-one"). Phosphorus (atomic number 15) is as follows: 1s 2 2s 2 2p 6 3s 2 3p 3. For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used.