If `Z_("eff")` of sodium is .x. then `Z_("eff")` of calcium is :-

Options

A. `x+0.35`
B. `x+0.65`
C. `x-0.35`
D. `x-0.65`

Explanation

To determine the effective nuclear charge (Z_eff) of calcium based on the given Z_eff of sodium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Z_eff**:
- The effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner-shell electrons.

2. **Given Information**:
- We know that Z_eff of sodium (Na) is given as X.
- Sodium has an atomic number of 11, and calcium (Ca) has an atomic number of 20.

3. **Group Classification**:
- Sodium belongs to Group 1 (alkali metals), while calcium belongs to Group 2 (alkaline earth metals).
- This indicates that calcium has an additional electron shell compared to sodium.

4. **Atomic Radii**:
- The atomic radius of sodium is approximately 1.02 Å, while the atomic radius of calcium is approximately 0.65 Å.
- The smaller radius of calcium suggests that its electrons are held more tightly by the nucleus compared to sodium.

5. **Calculating Z_eff for Calcium**:
- The Z_eff for calcium can be approximated by considering the Z_eff of sodium and adjusting for the difference in atomic radii.
- Since calcium has more protons (20) than sodium (11), we can express Z_eff of calcium in terms of Z_eff of sodium:
\[ Z_{eff} \text{ (Ca)} = Z_{eff} \text{ (Na)} + \text{(additional effect due to more protons)} \]
- Thus, if Z_eff of sodium is X, we can express Z_eff of calcium as:
\[ Z_{eff} \text{ (Ca)} = X + (0.65) \]

6. **Conclusion**:
- Therefore, the Z_eff of calcium can be stated as:
\[ Z_{eff} \text{ (Ca)} = X + 0.65 \]
- The correct option based on this calculation is option B.