Question

What are term symbols? What should I know about ground-state atomic term symbols?

Answer 1

Term symbols are used in spectroscopy to describe the electron configuration in terms of the total spin and the total orbital angular momentum.

An atomic term symbol, in the absence of a magnetic field for simplicity, is given as:

`""^(2S + 1) L`

where:

• `L = |sum_i m_l(i)|` is the total orbital angular momentum, and corresponds to an `S`, `P`, `D`, `F`, . . . state.
• `m_l(i)` is the magnetic quantum number for the `i`th electron that occupies a given atomic orbital.
• `S = |sum_i m_s(i)|` is the total spin angular momentum, and describes the total spin. `2S` describes the total number of unpaired electrons.
• `m_s(i)` is the spin quantum number for the `i`th electron that occupies a given atomic orbital.

So, if I were to give you a ground-state term symbol of `""^(4) S`, you should be able to recognize that

• `2S+1 = 4`, meaning there are `3` unpaired electrons.
• `L = 0`, meaning that all three `p` atomic orbitals of a given energy level are symmetrically occupied (`m_l = -1, 0, +1` sum to zero, and the magnitude of zero is zero) by single electrons each.

This would mean that `""^(4) S` corresponds to a `p^3` configuration. This would be like nitrogen atom.

Had I given you a `""^(4) F` ground-state term symbol, you should recognize that since `L = 3`, the first three `d` orbitals are occupied, of `m_l = -2, -1,` and `0` (the magnitude of `-3` is `3`). That came from:

`L = |(-2) + (-1) + (0)| = 3`

This would be like vanadium atom.

Or, if I asked you to determine the ground-state atomic term symbol for a `p^1` configuration, you would have:

`S = 1/2` for a single electron.
`L = |(-1)| = 1` for the first `p` orbital occupied, giving a `P` state.

Therefore, `""^(2(1/2)+1)P = color(blue)(""^(2) P)`, such as for the boron atom.