JEE Advanced · Chemistry · 4. Chemical Bonding

According to Molecular Orbital Theory,

A $C_{2}^{2 -}$ is expected to be diamagnetic
B $O_{2}^{2 +}$ is expected to have a longer bond length than $O_{2}$
C $N_{2}^{+}$ and $N_{2}^{-}$ have the same bond order
D $H e_{2}^{+}$ has the same energy as two isolated He atoms

Verified Solution

Answer & Solution

Correct Answer

(C) $N_{2}^{+}$ and $N_{2}^{-}$ have the same bond order

Step-by-step Solution

Detailed explanation

A] The molecular orbital energy configuration of

C_{2}^{2 -}

σ_{1 s}^{2}, σ_{1 s}^{* 2}, σ_{2 s}^{2}, σ_{2 s}^{* 2}, π_{2 p_{x}}^{2} = π_{2 p_{y}}^{2}, σ_{2 p_{z}}^{2}

In the MO of

C_{2}^{2 -}

there is no unpaired electron hence it is diamagnetic
B] Bond order of

O_{2}^{2 +}

is 3 and

O_{2}

is 2 therefore bond length of

O_{2}

is greater than

O_{2}^{2 +}

C] The molecular orbital energy configuration of

N_{2}^{+}

σ_{1 s}^{2}, σ_{1 s}^{* 2}, σ_{2 s}^{2}, σ_{2 s}^{* 2}, π_{2 p_{x}}^{2} = π_{2 p_{y}}^{2}, σ_{2 p_{z}}^{1}

Bond order of

N_{2}^{+} = \frac{1}{2} (9 - 4) = 2.5

The molecular orbital energy configuration of

N_{2}^{-}

σ_{1 s}^{2}, σ_{1 s}^{* 2}, σ_{2 s}^{2}, σ_{2 s}^{* 2}, π_{2 p_{x}}^{2} = π_{2 p_{y}}^{2}, σ_{2 p_{z}}^{2}, π_{2 p_{x}}^{* 1} = π_{2 p_{y}}^{*}

Bond order of

N_{2}^{-} = \frac{1}{2} (10 - 5) = 2.5

H e_{2}^{+}

has less energy as compare to two isolated He atoms

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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	List- $I$		List- $II$
$(I)$	Probability of $(X_{2} \geq Y_{2})$ is	$(P)$	$\frac{3}{8}$
$(II)$	Probability of $(X_{2} > Y_{2})$ is	$(Q)$	$\frac{11}{16}$
$(III)$	Probability of $(X_{3} = Y_{3})$ is	$(R)$	$\frac{5}{16}$
$(IV)$	Probability of $(X_{3} > Y_{3})$ is	$(S)$	$\frac{355}{864}$
		$(T)$	$\frac{77}{432}$