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`

Answer

To solve the problem of finding the effective nuclear charge (\(Z_{eff}\)) of calcium given that the \(Z_{eff}\) of sodium is \(x\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Effective Nuclear Charge (\(Z_{eff}\))**:
- The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons.

2. **Identify the Elements**:
- Sodium (Na) has an atomic number of 11.
- Calcium (Ca) has an atomic number of 20.

3. **Determine the Position in the Periodic Table**:
- Both sodium and calcium are in the s-block of the periodic table. Sodium is in Group 1, while calcium is in Group 2.

4. **Consider the Trend in Effective Nuclear Charge**:
- As we move down a group in the periodic table, the effective nuclear charge generally increases due to the increase in the number of protons, but the shielding effect also increases because of the additional electron shells.

5. **Calculate the Change in \(Z_{eff}\)**:
- Given that the \(Z_{eff}\) of sodium is \(x\), we need to find the \(Z_{eff}\) of calcium.
- The video transcript mentions that the radius of calcium contributes an additional value of 0.65 to the \(Z_{eff}\) of sodium.

6. **Formulate the Equation**:
- Therefore, the effective nuclear charge of calcium can be expressed as:
\[ Z_{eff} \text{ of Ca} = Z_{eff} \text{ of Na} + 0.65 \]
- Substituting the known value:
\[ Z_{eff} \text{ of Ca} = x + 0.65 \]

7. **Select the Correct Option**:
- Based on the options provided, the correct answer is:
\[ Z_{eff} \text{ of Ca} = x + 0.65 \]
- Thus, the answer corresponds to option 2.

### Final Answer:
The \(Z_{eff}\) of calcium is \(x + 0.65\).