Step 1: Understanding the Concept:
According to Molecular Orbital (MO) Theory, atomic orbitals combine to form bonding and antibonding molecular orbitals.
Electrons are filled into these orbitals based on the Aufbau principle, Hund's rule, and Pauli's exclusion principle.
Antibonding molecular orbitals (denoted with an asterisk, e.g., \(\sigma^*\), \(\pi^*\)) have higher energy and contain nodal planes between the nuclei.
Step 2: Key Formula or Approach:
Write the MO electronic configuration for each diatomic molecule and count the total number of electrons in antibonding orbitals.
The general order for filling orbitals for molecules like Li\(_2\), N\(_2\) is: \(\sigma 1s, \sigma^* 1s, \sigma 2s, \sigma^* 2s, (\pi 2p_x = \pi 2p_y), \sigma 2p_z, (\pi^* 2p_x = \pi^* 2p_y), \sigma^* 2p_z\).
For O\(_2\) and F\(_2\), the \(\sigma 2p_z\) orbital is lower in energy than the \(\pi 2p\) orbitals.
Step 3: Detailed Explanation:
(A) Li\(_2\): Total electrons = 6. Configuration: \(\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2\).
Antibonding electrons = 2 (in \(\sigma^* 1s\)).
(B) N\(_2\): Total electrons = 14. Configuration: \(\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, (\pi 2p_x^2 = \pi 2p_y^2), \sigma 2p_z^2\).
Antibonding electrons = 2 + 2 = 4 (in \(\sigma^* 1s\) and \(\sigma^* 2s\)).
(C) O\(_2\): Total electrons = 16. Configuration: \(\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, (\pi 2p_x^2 = \pi 2p_y^2), (\pi^* 2p_x^1 = \pi^* 2p_y^1)\).
Antibonding electrons = 2 + 2 + 1 + 1 = 6.
(D) F\(_2\): Total electrons = 18. Configuration: \(\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, (\pi 2p_x^2 = \pi 2p_y^2), (\pi^* 2p_x^2 = \pi^* 2p_y^2)\).
Antibonding electrons = 2 + 2 + 2 + 2 = 8.
Comparing the results, fluorine (F\(_2\)) has the maximum of 8 antibonding electrons.
Step 4: Final Answer:
The molecule F\(_2\) contains the maximum number (8) of electrons in its antibonding molecular orbitals.