In the following questions, a statement of assertion (A) is followed by a statement of reason (R )
A : Bond order of `H_(2)^(+)` is 0.5
R : Electrons are removed from the antibonding molecular orbital from `H_(2)` .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To solve the question, we will analyze the assertion (A) and the reason (R) step by step.

### Step 1: Analyze the Assertion (A)
The assertion states that the bond order of \( H_2^+ \) is 0.5.

**Bond Order Calculation:**
- The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \left( N_b - N_a \right) \]
where \( N_b \) is the number of electrons in bonding molecular orbitals and \( N_a \) is the number of electrons in antibonding molecular orbitals.

- For \( H_2^+ \), there is 1 electron in the bonding molecular orbital (σ 1s) and 0 electrons in the antibonding molecular orbital (σ* 1s).

- Therefore, substituting the values:
\[ \text{Bond Order} = \frac{1}{2} \left( 1 - 0 \right) = \frac{1}{2} = 0.5 \]

**Conclusion for Assertion:**
- The assertion is **true**.

### Step 2: Analyze the Reason (R)
The reason states that electrons are removed from the antibonding molecular orbital of \( H_2 \).

**Understanding Electron Removal:**
- In the case of \( H_2 \), there are 2 electrons, both of which occupy the bonding molecular orbital (σ 1s).

- When forming \( H_2^+ \), one electron is removed. Since both electrons in \( H_2 \) are in the bonding orbital, the electron that is removed comes from the bonding molecular orbital, not the antibonding one.

**Conclusion for Reason:**
- The reason is **false** because the electron is removed from the bonding orbital, not the antibonding orbital.

### Final Conclusion
- The assertion (A) is true, while the reason (R) is false. Therefore, the correct answer is that the assertion is true, but the reason is false.

### Summary of the Solution:
1. The bond order of \( H_2^+ \) is calculated to be 0.5, making the assertion true.
2. The reason incorrectly states that electrons are removed from the antibonding orbital; they are actually removed from the bonding orbital, making the reason false.