Question

The bond order of $\text{Li}_2$ is _______ and it is _______.

• A. 1, diamagnetic
• B. 2, paramagnetic
• C. 1, paramagnetic
• D. 2, diamagnetic

Hint:

For light homonuclear diatomic molecules, if the total number of electrons is even (except for $B_2$ with 10 electrons and $O_2$ with 16 electrons), the molecule is almost always diamagnetic.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the bond order and magnetic nature of the dilithium ($\text{Li}_2$) molecule.
This is solved using the principles of Molecular Orbital Theory (MOT).

Step 2: Key Formula or Approach:
The bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{N_b - N_a}{2} \]
Where $N_b$ is the number of bonding electrons and $N_a$ is the number of anti-bonding electrons.
Magnetic behavior is determined by the presence of unpaired electrons:
- Paramagnetic: At least one unpaired electron.
- Diamagnetic: All electrons are paired.

Step 3: Detailed Explanation:

• Lithium (Li) has an atomic number of 3, with an electronic configuration of $1s^2 2s^1$.

• A neutral $\text{Li}_2$ molecule has a total of 6 electrons ($3 \times 2 = 6$).

• According to Molecular Orbital Theory, the 6 electrons are filled into molecular orbitals in order of increasing energy:
\[ \sigma_{1s}^2 \ \sigma_{1s}^{*2} \ \sigma_{2s}^2 \]

• Let us identify the number of bonding and anti-bonding electrons:
- Bonding orbitals ($\sigma_{1s}, \sigma_{2s}$) contain: $2 + 2 = 4$ electrons ($N_b = 4$).
- Anti-bonding orbital ($\sigma_{1s}^*$) contains: 2 electrons ($N_a = 2$).

• Now, calculate the bond order:
\[ \text{Bond Order} = \frac{4 - 2}{2} = \frac{2}{2} = 1 \]

• Next, we check for unpaired electrons in the molecular orbital configuration.

• Since all occupied molecular orbitals ($\sigma_{1s}$, $\sigma_{1s}^*$, $\sigma_{2s}$) contain exactly two electrons, all 6 electrons are paired.

• Because there are no unpaired electrons, the $\text{Li}_2$ molecule is diamagnetic.


Step 4: Final Answer:
The bond order of $\text{Li}_2$ is 1, and its magnetic nature is diamagnetic.