Which one of the following molecules is expected to exhibit diamagnetic behaviour?
(a) C2
(b) N2
(c)

Q: Why does the energy order of molecular orbitals change after nitrogen?

It's all about s-p mixing! In atoms like B, C, and N, the 2s and 2p orbitals are close in energy, causing them to mix. This pushes the $\sigma_{2p_z}$ orbital higher in energy, above the $\pi_{2p}$ orbitals. In O and F, the energy gap is larger, so mixing is negligible, and $\sigma_{2p_z}$ stays below $\pi_{2p}$.

Q: Why is $O_2$ paramagnetic even though 16 is an even number?

This is a classic trap! Even numbers don't guarantee pairing. Because the two $\pi^*_{2p}$ orbitals have the exact same energy (degenerate), Hund's Rule dictates that electrons must occupy them singly before pairing up. Thus, $O_2$ gets two unpaired electrons.

Q: Does $S_2$ behave exactly like $O_2$?

Yes! Sulfur is right below oxygen in the periodic table. Its valence electrons are in the 3s and 3p orbitals, but the molecular orbital diagram follows the exact same pattern as $O_2$, resulting in two unpaired electrons and paramagnetic behavior.

Q: What does the bond order of $C_2$ tell us?

The bond order of $C_2$ is 2, which means it has a double bond. But here's the fascinating part: both of these bonds are $\pi$ bonds! There is no $\sigma$ bond in $C_2$ because the $\sigma_{2s}$ and $\sigma^*_{2s}$ cancel each other out, and the highest occupied orbitals are purely $\pi$.

Q: Can we predict magnetic behavior just by looking at the total number of electrons?

As a quick trick, molecules with an odd number of electrons are always paramagnetic. Molecules with an even number of electrons are usually diamagnetic, EXCEPT for those with 10 or 16 electrons (like $B_2$ and $O_2$), which are paramagnetic due to Hund's rule in degenerate orbitals.

Question

Which one of the following molecules is expected to exhibit diamagnetic behaviour?

Options:

(A) $C_2$

(B) $N_2$

(C) $O_2$

(D) $S_2$

Sigma Percentile · Accepted Answer

### Unveiling the Magnetic Secrets of Diatomic Molecules

When we dive into the quantum world of molecules, their magnetic properties often reveal fascinating stories about their internal electron arrangements. The key to unlocking these secrets lies in **Molecular Orbital (MO) Theory**.

In this problem, we are tasked with identifying which of the given diatomic molecules ($C_2$, $N_2$, $O_2$, $S_2$) exhibit **diamagnetic behavior**. Let's break down the physics and chemistry behind this.

### The Rule of Magnetism

Before we look at the molecules, we must establish the ground rules of magnetism at the molecular level:
*   **Diamagnetic:** A molecule is diamagnetic if **all** of its electrons are paired up in their respective orbitals. These molecules are weakly repelled by a magnetic field.
*   **Paramagnetic:** A molecule is paramagnetic if it contains **at least one unpaired electron**. These molecules are attracted to a magnetic field.

To determine the pairing of electrons, we must construct the molecular orbital electronic configuration for each candidate.

### The $\le 14$ Electron Club: $C_2$ and $N_2$

For homonuclear diatomic molecules with 14 or fewer electrons, a phenomenon known as **s-p mixing** plays a crucial role. Because the $2s$ and $2p$ atomic orbitals are relatively close in energy, they interact, pushing the $\sigma_{2p_z}$ molecular orbital higher in energy—specifically, above the degenerate $\pi_{2p_x}$ and $\pi_{2p_y}$ orbitals.

The energy sequence is:
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z}$$

Let's analyze **$C_2$**:
Carbon has 6 electrons, so $C_2$ has a total of 12 electrons. Filling them in order:
$$C_2: \sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \pi_{2p_x}^2 = \pi_{2p_y}^2$$
Notice that the last four electrons perfectly fill the $\pi_{2p}$ orbitals. Since every single electron has a partner, **$C_2$ is diamagnetic**.

Now, let's look at **$N_2$**:
Nitrogen has 7 electrons, giving $N_2$ a total of 14 electrons. We simply add two more electrons to the $C_2$ configuration:
$$N_2: \sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \pi_{2p_x}^2 = \pi_{2p_y}^2, \sigma_{2p_z}^2$$
Once again, the $\sigma_{2p_z}$ orbital is fully occupied. All electrons are paired, making **$N_2$ diamagnetic** as well.

### The $> 14$ Electron Club: $O_2$ and $S_2$

As we move across the periodic table to oxygen and fluorine, the energy gap between the $2s$ and $2p$ orbitals widens significantly. This drastically reduces s-p mixing, allowing the $\sigma_{2p_z}$ orbital to drop back down below the $\pi_{2p}$ orbitals.

The new energy sequence is:
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y}$$

Let's analyze **$O_2$**:
Oxygen has 8 electrons, so $O_2$ has 16 electrons. Let's fill the orbitals:
$$O_2: \sigma_{1s}^2, \sigma^*_{1s}^2, \sigma_{2s}^2, \sigma^*_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2 = \pi_{2p_y}^2, \pi^{*1}_{2p_x} = \pi^{*1}_{2p_y}$$
Here lies the trap! We have two electrons left to place in the degenerate $\pi^*$ anti-bonding orbitals. According to **Hund's Rule of Maximum Multiplicity**, electrons will occupy degenerate orbitals singly before pairing up. Therefore, $O_2$ has **two unpaired electrons**, making it strictly **paramagnetic**.

The same logic applies to **$S_2$**. Although sulfur uses $3s$ and $3p$ orbitals, its valence molecular orbital diagram is structurally identical to oxygen's, resulting in two unpaired electrons and paramagnetic behavior.

### Conclusion

By meticulously applying Molecular Orbital Theory, we have successfully deduced that both $C_2$ and $N_2$ have fully paired electron configurations, rendering them diamagnetic. Conversely, $O_2$ and $S_2$ harbor unpaired electrons, making them paramagnetic. Thus, the correct choices are (a) and (b).

Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: Which one of the following molecules is expected to exhibit diamagnetic behaviour?

Select Answer:

Visualized Solution

Magnetic Behavior

MO Energy Order ( $Z \leq 14$ )

Analyzing $C_{2}$

Analyzing $N_{2}$

MO Energy Order ( $Z > 14$ )

Analyzing $O_{2}$ and $S_{2}$

Final Conclusion

The Sigma Insight: Molecular Orbital Theory

Unveiling the Magnetic Secrets of Diatomic Molecules

The Rule of Magnetism

The $\leq 14$ Electron Club: $C_{2}$ and $N_{2}$

The $> 14$ Electron Club: $O_{2}$ and $S_{2}$

Conclusion

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