Question

According to molecular theory, the species among the following that does not exist is:

• A. $He _{2}^{+}$
• B. $He _{2}^{-}$
• C. $Be _{2}$
• D. $O _{2}^{2-}$

Answer 1

The Correct Option is C

 To determine which species does not exist according to molecular orbital theory, we need to understand the stability of these molecular ions and molecules based on their electron configurations.

1. \(He_2^+\) (Helium molecular ion):
   • Helium has an atomic number of 2, so each helium atom contributes 2 electrons.
   • In \(He_2^+\), there are 3 electrons (since it is positively charged).
   • The molecular orbital configuration is: \(\sigma_{1s}^2, \sigma^*_{1s}^1\).
   • Bond order = (Bonding electrons - Antibonding electrons)/2 = (2 - 1)/2 = 0.5.
   • A positive bond order indicates that \(He_2^+\) can exist.
2. \(He_2^−\) (Helium molecular ion):
   • In \(He_2^−\), there are 5 electrons (since it is negatively charged).
   • The molecular orbital configuration is: \(\sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^1\).
   • Bond order = (Bonding electrons - Antibonding electrons)/2 = (3 - 2)/2 = 0.5.
   • A positive bond order indicates that \(He_2^−\) can exist.
3. \(Be_2\) (Beryllium molecule):
   • Beryllium has an atomic number of 4, and therefore each beryllium atom contributes 4 electrons, totaling 8 electrons for \(Be_2\).
   • The molecular orbital configuration is: \(\sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2\).
   • Bond order = (Bonding electrons - Antibonding electrons)/2 = (4 - 4)/2 = 0.
   • A bond order of zero indicates that \(Be_2\) does not exist.
4. \(O_2^{2-}\) (Peroxide ion):
   • Oxygen has an atomic number of 8. Each oxygen contributes 8 electrons, so \(O_2^{2-}\) has 18 electrons.
   • The molecular orbital configuration is: \(\sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2, \pi^*_{2p_x}^2, \pi^*_{2p_y}^2\).
   • Bond order = (Bonding electrons - Antibonding electrons)/2 = (10 - 8)/2 = 1.
   • A positive bond order indicates that \(O_2^{2-}\) can exist.

In conclusion, \(Be_2\) does not exist due to its bond order being zero, which implies no net bonding interaction between the beryllium atoms. Therefore, the correct answer is \(Be_2\).