Question

Arrange the following species in the correct order of their stability $C_2 , Li_2, O_2^{+} , He_2^{+}$

• A. $Li_2 < He_2^{+} < O_2^{+} < C_2$
• B. $C_2< O_2^{+} < Li_2 < He_2^{+}$
• C. $ He_2^{+} < Li_2< C_2 < O_2^{+}$
• D. $O_2^{+} < C_2< Li_2 < He_2^{+}$
• E. $C_2 < Li_2 < He_2^{+} < O_2^{+}$

Answer 1

Answer: (C)

Higher the bond order, more is the stability. The bond order of the given species can be calculated as

$MO$ configuration of $C_{2}=(6+6=12)$

$=\sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 s^{2}, \pi 2 p_{x}^{2} \approx \pi 2 p_{Y}^{2} $

$B O =\frac{N_{b}-N_{a}}{2}=\frac{8-4}{2}=\frac{4}{2}=2$

$MO$ configuration of $Li _{2}=(3+3=6)$

$=\sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2} $

$BO =\frac{4-2}{2}=1$

$MO$ configuration of $O _{2}(8+8-1=15)$

$=\sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 s^{2}, \sigma 2 p_{z}^{2}, \pi 2 p_{x}^{2}$

$\approx \pi 2 p_{Y^{'}}^{2}, \pi^{*} 2 p_{x}^{1}$

$BO =\frac{10-5}{2}=2.5$

$MO$ configuration of $He _{2}=(2+2-1=3)$

$=\sigma 1 s^{2}, \sigma^{*} 1 s^{1} $

$BO =\frac{2-1}{2}=\frac{1}{2}=0.5$

Thus, the order of bond orders of the given species is

$He _{2}^{+}< Li _{2}< C _{2}< O _{2}^{+}$

Since, bond order $\alpha$ stability.

Thus, order of stability will also be the same.