Two of the three electrons in a lithium atom have quantum numbers `(n, l, m_(l), m_(s))` of (`1,0,0,+1//2)` and `(1,0,0,-1//2)`. What quantum numbers are possible for the third electron if the atom is (a) in the ground state and (b) in the first excited state?

Explanation

To solve the problem, we need to determine the possible quantum numbers for the third electron in a lithium atom under two conditions: (a) when the atom is in the ground state and (b) when it is in the first excited state.

### Step-by-Step Solution:

#### (a) Ground State Configuration of Lithium Atom

1. **Identify the Ground State Configuration**:
The ground state electron configuration of lithium (Li) is \(1s^2 2s^1\). This means that:
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