For which of the following species sum of spin quantum numbers of all electrons comes out to be zero ?

Options

A. `Cr^(+)(Z=24)`
B. `Sc(Z=21)`
C. `Cu^(+)(Z=29)`
D. `Na(Z=11)`

Explanation

To determine which of the given species has a sum of spin quantum numbers of all electrons equal to zero, we need to analyze the electronic configurations of each species and check if all electrons are paired.

### Step-by-Step Solution:

1. **Understand Spin Quantum Numbers**:
- Each electron has a spin quantum number of either +1/2 or -1/2. For a sum of spin quantum numbers to be zero, all electrons must be paired (one with +1/2 and one with -1/2).

2. **Analyze Each Species**:
- We will analyze the electronic configurations of the given species to check for paired electrons.

3. **Chromium Ion (Cr⁺)**:
- Chromium (Cr) has an atomic number of 24. Its electronic configuration is:
- Cr: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹
- For Cr⁺, we remove one electron from the 4s orbital:
- Cr⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵
- The 3d subshell has 5 unpaired electrons (one in each of the five d orbitals). Thus, the sum of the spin quantum numbers is not zero.

4. **Scandium (Sc)**:
- Scandium (Sc) has an atomic number of 21. Its electronic configuration is:
- Sc: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹
- The 3d subshell has 1 unpaired electron. Thus, the sum of the spin quantum numbers is not zero.

5. **Copper (Cu)**:
- Copper (Cu) has an atomic number of 29. Its electronic configuration is:
- Cu: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s¹
- The 3d subshell is fully filled (10 paired electrons), but the 4s subshell has 1 unpaired electron. Thus, the sum of the spin quantum numbers is not zero.

6. **Sodium (Na)**:
- Sodium (Na) has an atomic number of 11. Its electronic configuration is:
- Na: 1s² 2s² 2p⁶ 3s¹
- The 3s subshell has 1 unpaired electron. Thus, the sum of the spin quantum numbers is not zero.

### Conclusion:
None of the species listed (Cr⁺, Sc, Cu, Na) have a sum of spin quantum numbers equal to zero, as all have unpaired electrons.