Question

Hi! I have a question about the electronic configuration. For example, when i have a neutral carbon (Z = 6) configuration (1s^2)(2s^2)(2p^2), what is the term symbol for it(consistent with total antisymmetry of the state)?

Answer 1

Answer 2

To determine the term symbol for a neutral carbon atom with electronic configuration (1s^2)(2s^2)(2p^2), we need to consider the following rules:

1. Hund's Rule: In the ground state, electrons will occupy degenerate orbitals (orbitals with the same energy) in a way that maximizes the total spin.

2. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers, including the spin quantum number (ms).

3. L-S Coupling: For atoms with multiple electrons, we couple the orbital angular momentum (L) and the electron spin (S) to get the total angular momentum (J).

The electron configuration of carbon is (1s^2)(2s^2)(2p^2), which means there are two electrons in the 2p subshell.

Let's list the possible quantum numbers for the two 2p electrons:

Electron 1: (n = 2, l = 1, m_l = -1, m_s = +1/2) Electron 2: (n = 2, l = 1, m_l = +1, m_s = -1/2)

Now, we need to combine these quantum numbers to obtain the term symbol.

Since there are two electrons in the 2p subshell, the total spin quantum number S can be either 1 (if the spins are parallel, aligned in the same direction) or 0 (if the spins are antiparallel, aligned in opposite directions).

Now, let's consider the possible combinations of the quantum numbers for S = 1:

1. Electrons with m_s = +1/2 and -1/2 (parallel spins): (n = 2, l = 1, S = 1, L = 1, J = 2)

2. Electrons with m_s = -1/2 and +1/2 (parallel spins): (n = 2, l = 1, S = 1, L = 1, J = 2)

Since both combinations give the same term symbol, we write the term symbol as follows:

^3P

The term symbol ^3P represents the ground state of a carbon atom. The superscript 3 indicates the total angular momentum J = 2S + 1, which is 3 in this case, and the letter P represents the orbital angular momentum L.