Question

Identify a molecule which does not exist.

• A. $He_2$
• B. $Li_2$
• C. $C_2$
• D. $O_2$

Answer 1

The Correct Option is A

To determine which molecule does not exist among the given options, we need to consider concepts of molecular bonding and stability, especially focusing on the molecular orbital (MO) theory and electronic configurations.

1. Understanding Molecular Stability: Molecular Orbital Theory
   • Molecules exist if their formation leads to more stability. In terms of molecular orbitals, a molecule will form if there are more electrons in bonding orbitals than in antibonding orbitals.
   • The stability of a diatomic molecule can often be predicted based on the bond order: \(\text{Bond order} = \frac{\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}}{2}\).
   • If bond order > 0, the molecule is likely to be stable and exist; if bond order = 0, the molecule does not exist.
2. Analysis of Given Molecules:
   • \(He_2\):
     • Helium has two electrons per atom. In the diatomic molecule \(He_2\), the total number of electrons is 4.
     • Filling the molecular orbitals, these electrons would completely fill the bonding and antibonding orbitals equally (2 electrons each in \(\sigma_{1s}\uparrow \downarrow\) and \(\sigma_{1s}^*\uparrow \downarrow\)).
     • Calculation of bond order: \(\text{Bond order} = \frac{2 - 2}{2} = 0\).
     • Since the bond order is 0, \(He_2\) does not exist.
   • \(Li_2\):
     • Lithium has three electrons per atom. For \(Li_2\), there are a total of 6 electrons.
     • Molecular orbitals are filled as \(\sigma_{1s}\uparrow \downarrow, \sigma_{1s}^*\uparrow \downarrow, \sigma_{2s}\uparrow \downarrow\).
     • Calculation of bond order: \(\text{Bond order} = \frac{4 - 2}{2} = 1\).
     • Since the bond order is 1, \(Li_2\) exists.
   • \(C_2\):
     • Carbon has six electrons per atom. Thus, \(C_2\) has 12 electrons in total.
     • Molecular orbitals filled as: \(\sigma_{1s}\uparrow \downarrow, \sigma_{1s}^*\uparrow \downarrow, \sigma_{2s}\uparrow \downarrow, \sigma_{2s}^*\uparrow \downarrow, \pi_{2px}\uparrow \downarrow, \pi_{2py}\uparrow \downarrow\).
     • Calculation of bond order: \(\text{Bond order} = \frac{8 - 4}{2} = 2\).
     • Since the bond order is 2, \(C_2\) exists.
   • \(O_2\):
     • Oxygen has eight electrons per atom. For \(O_2\), 16 electrons in total.
     • Filling molecular orbitals yields a bond order of 2, making it stable and existent.

Conclusion: Based on the molecular orbital theory and bond order calculations, the molecule \(He_2\) does not exist because its bond order is zero, while the other molecules have positive bond orders indicating their stability and existence.