Assertion: `Yb^(+2)` is more stable in compare to `Gd^(+2)`
Reason: The electronic configuration of Gd is [Xe]`4f^(7)5d^(2)6s^(2)`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reson are true but reason is not the correct explanation of assertion.
C. if assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the problem, we need to analyze the assertion and the reason provided in the question regarding the stability of the ions \(Yb^{+2}\) and \(Gd^{+2}\).

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that \(Yb^{+2}\) is more stable compared to \(Gd^{+2}\).
- To evaluate this, we need to look at the electronic configurations of both ions.

2. **Electronic Configuration of Ytterbium (Yb)**:
- The atomic number of Ytterbium (Yb) is 70.
- The electronic configuration of neutral Yb is:
\[ [Xe] 4f^{14} 6s^{2} \]
- When Yb loses two electrons to form \(Yb^{+2}\), the configuration becomes:
\[ [Xe] 4f^{14} 6s^{0} \]
- This means that \(Yb^{+2}\) has a fully filled \(4f\) subshell, which is generally more stable.

3. **Electronic Configuration of Gadolinium (Gd)**:
- The atomic number of Gadolinium (Gd) is 64.
- The electronic configuration of neutral Gd is:
\[ [Xe] 4f^{7} 5d^{1} 6s^{2} \]
- When Gd loses two electrons to form \(Gd^{+2}\), the configuration becomes:
\[ [Xe] 4f^{7} 5d^{1} 6s^{0} \]
- Here, \(Gd^{+2}\) has a half-filled \(4f\) subshell and a partially filled \(5d\) subshell.

4. **Comparing Stability**:
- The stability of electron configurations is influenced by the filling of subshells.
- Fully filled subshells (like \(4f^{14}\) in \(Yb^{+2}\)) are more stable than half-filled subshells (like \(4f^{7}\) in \(Gd^{+2}\)).
- Therefore, \(Yb^{+2}\) is indeed more stable than \(Gd^{+2}\).

5. **Analyzing the Reason**:
- The reason states that the electronic configuration of Gd is \([Xe] 4f^{7} 5d^{2} 6s^{2}\).
- This statement is incorrect; the correct configuration is \([Xe] 4f^{7} 5d^{1} 6s^{2}\).

6. **Conclusion**:
- The assertion is true: \(Yb^{+2}\) is more stable than \(Gd^{+2}\).
- The reason is false: the electronic configuration of Gd is incorrectly stated.
- Therefore, the correct conclusion is that the assertion is true, but the reason is false.

### Final Answer:
The correct option is C: "Assertion is true but reason is false."