Suppose two electrons in an atom have quantum numbers `n=2` and `l=1`. (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable). (b) If the Pauli exclusion principle did not apply to the electrons, how many states would be possible?

Explanation

To solve the problem, we need to determine the number of possible states for two indistinguishable electrons with given quantum numbers \( n = 2 \) and \( l = 1 \).

### Part (a): How many states are possible for those two electrons?

1. **Identify the quantum numbers**:
- Principal quantum number \( n = 2 \)
- Orbital quantum number \( l = 1 \)
- The magnetic quantum number \( m_l \) can take values from \( -l \) to \( +l \), which gives us \( m_l = -1, 0, 1 \) (3 possible values).
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