Step 1: Understanding Molecular Orbital Theory. According to Molecular Orbital (MO) theory, paramagnetism occurs when a molecule has one or more unpaired electrons in its molecular orbitals. These unpaired electrons create a magnetic field, making the molecule attracted to a magnetic field (paramagnetic behavior). Diamagnetic molecules, on the other hand, have all their electrons paired and do not exhibit such attraction.
Step 2: Molecular Orbitals for Diatomic Molecules. Let’s apply the molecular orbital theory to the given molecules to check for unpaired electrons.
1. Oxygen ({ O }₂):
The electronic configuration for { O }₂ (in the molecular orbital theory) is:
( \sigma ₁s², \sigma ^{₁s}², \sigma ₂s², \sigma ^{₂s}², \pi ₂p̀x;², \pi ₂p̀y;², \pi ^{₂p̀x;}¹, \pi ^{₂p̀y;}¹ ) Here, the two \pi -antibonding orbitals each have one unpaired electron, making { O }₂ paramagnetic.
2. Nitrogen ({ N }₂):
The electronic configuration for { N }₂ is:
( \sigma ₁s², \sigma ^{₁s}², \sigma ₂s², \sigma ^{₂s}², \pi ₂p̀x;², \pi ₂p̀y;² ) All electrons in { N }₂ are paired, so it is diamagnetic and does not exhibit paramagnetism.
3. Fluorine ({ F }₂):
The electronic configuration for { F }₂ is:
( \sigma ₁s², \sigma ^{₁s}², \sigma ₂s², \sigma ^{₂s}², \pi ₂p̀x;², \pi ₂p̀y;², \pi ^{₂p̀x;}², \pi ^{₂p̀y;}² ) All electrons are paired in { F }₂, so it is diamagnetic and does not exhibit paramagnetism.
4. Carbon ({ C }₂):
The electronic configuration for { C }₂ is:
( \sigma ₁s², \sigma ^{₁s}², \sigma ₂s², \sigma ^{₂s}², \pi ₂p̀x;², \pi ₂p̀y;² ) All electrons are paired in { C }₂, so it is diamagnetic and does not exhibit paramagnetism.
Step 3: Conclusion. Based on the molecular orbital theory, { O }₂ has unpaired electrons and exhibits paramagnetism. The correct answer is (1) { O }₂.