Question

According to molecular orbital theory, which of the following is true with respect to \(\mathrm{Li_2^+}\) and \(\mathrm{Li_2^-}\) ?

• A. \(\mathrm{Li_2^+}\) is unstable and \(\mathrm{Li_2^-}\) is stable
• B. \(\mathrm{Li_2^+}\) is stable and \(\mathrm{Li_2^-}\) unstable
• C. Both are stable
• D. Both are unstable

Hint:

Count the electrons, fill the MOs and compute bond order; a positive bond order means stable.

Answer 1

The Correct Option is C

Li₂ MO order: \(\sigma1s\lt\sigma^*1s\lt\sigma2s\lt\sigma^*2s\).
\(\mathrm{Li_2^+}\): 5 electrons, \(\sigma1s^2\,\sigma^*1s^2\,\sigma2s^1\): bond order = (3 - 2)/2 = 0.5 (stable).
\(\mathrm{Li_2^-}\): 7 electrons, \(\sigma1s^2\,\sigma^*1s^2\,\sigma2s^2\,\sigma^*2s^1\): bond order = (4 - 3)/2 = 0.5 (stable).
Both have bond order 0.5 > 0, so both are stable.
Answer: (3) Both are stable