Question

Given below are two statements
Statement-I: In the conversion of \(O_2^+\) to \(O_2^{2+}\) bond length increases
Statement-II: In the conversion of \(O_2^+\) to \(O_2^{2+}\) magnetic property changes

• A. Both statements I and II are correct
• B. Statement I is correct, but statement II is not correct
• C. Statement I is not correct, but statement II is correct
• D. Both statements I and II are not correct \bigskip

Hint:

\[ BO(O_2)=2 \] \[ BO(O_2^+)=2.5 \] \[ BO(O_2^{2+})=3 \] Increasing bond order implies decreasing bond length.

Answer 1

The Correct Option is C

Concept: According to Molecular Orbital Theory, \[ Bond\ Order= \frac{N_b-N_a}{2} \] where \[ N_b=\text{bonding electrons} \] \[ N_a=\text{antibonding electrons} \] Higher bond order means stronger bond and smaller bond length.

Step 1: Determine bond order of \(O_2^+\).
For \(O_2\), \[ Bond\ Order=2 \] Removing one electron from antibonding orbital gives \[ O_2^+ \] Therefore, \[ Bond\ Order=2.5 \]

Step 2: Determine bond order of \(O_2^{2+}\).
Removing one more electron from antibonding orbital: \[ O_2^{2+} \] Hence, \[ Bond\ Order=3 \]

Step 3: Check Statement-I.
Bond order increases from \[ 2.5 \rightarrow 3 \] As bond order increases, bond length decreases. Therefore the statement \[ \text{``bond length increases''} \] is false. Hence Statement-I is incorrect.

Step 4: Check Statement-II.
\(O_2^+\) contains one unpaired electron. Hence it is \[ \text{Paramagnetic} \] \(O_2^{2+}\) contains no unpaired electron. Hence it is \[ \text{Diamagnetic} \] Therefore magnetic property changes. Statement-II is correct.

Step 5: Choose the correct option.
Statement-I is false. Statement-II is true. Thus, \[ \boxed{\text{Option (C)}} \]