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. $O_2^{+} < C_2< Li_2 < He_2^{+}$

Answer 1

The Correct Option is C

The correct option is(C): \(He_2^{+} < Li_2< C_2 < O_2^{+}\).

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.