Given this set of quantum numbers for a multi electron atom `2, 0, 0, and -1//2`. The next higher allowed set of n and 1 for this atom in its ground state

Options

A. n=2, l=0
B. n=2, l=1
C. n=3, l = 1
D. n=3, l=1

Answer

To solve the problem, we need to identify the next higher allowed set of quantum numbers (n and l) for a multi-electron atom given the initial set of quantum numbers: \( n = 2 \), \( l = 0 \), \( m_l = 0 \), and \( m_s = -\frac{1}{2} \).

### Step-by-Step Solution:

1. **Identify the Given Quantum Numbers**:
- The given quantum numbers are:
- Principal quantum number (\( n \)) = 2
- Azimuthal quantum number (\( l \)) = 0
- Magnetic quantum number (\( m_l \)) = 0
- Spin quantum number (\( m_s \)) = -\(\frac{1}{2}\)

2. **Determine the Subshell**:
- The azimuthal quantum number \( l = 0 \) corresponds to the s subshell. Therefore, the given state is in the 2s subshell.

3. **Find the Next Higher Subshell**:
- The next higher subshell after 2s is 2p.
- For the 2p subshell, the values of \( n \) and \( l \) are:
- \( n = 2 \) (the principal quantum number remains the same)
- \( l = 1 \) (for p subshell)

4. **Conclusion**:
- The next higher allowed set of quantum numbers for this atom in its ground state is:
- \( n = 2 \)
- \( l = 1 \)

### Final Answer:
The next higher allowed set of quantum numbers is \( n = 2 \) and \( l = 1 \).

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