Answer to Question #279319 in Atomic and Nuclear Physics for BIGIRIMANA Elie

Question

What are the quantum numbers for the electrons in the lithium atom (Z =

3) when the atom is in its ground state?

and do the Same question as 5 for Sodium (Z = 11).

Answer 1

The electron configuration of lithium is 1s²2s¹

The quantum number sets are:

For two 1s-electrons: (1, 0, 0, $\frac{1}{2}$), (1, 0, 0, -$\frac{1}{2}$)

For 2s-electron: (2, 0, 0, $\frac{1}{2}$) or (2, 0, 0, -$\frac{1}{2}$)

The electron configuration of sodium is 1s²2s²2p⁶3s¹

The quantum number sets are:

For two 1s-electrons: (1, 0, 0, $\frac{1}{2}$), (1, 0, 0, -$\frac{1}{2}$)

For two 2s-electrons: (2, 0, 0, $\frac{1}{2}$), (2, 0, 0, -$\frac{1}{2}$)

For six 2p-electrons: (3, 1, -1, $\frac{1}{2}$), (3, 1, -1, -$\frac{1}{2}$), (3, 1, 0, $\frac{1}{2}$), (3, 1, 0, -$\frac{1}{2}$), (3, 1, 1, $\frac{1}{2}$), (3, 1, 1, -$\frac{1}{2}$)

For 3s-electron: (3, 0, 0, $\frac{1}{2}$) or (3, 0, 0, -$\frac{1}{2}$)

All quantum number sets are written in the form (n, l, m_l, m_s).