Q.State and explain Hund's rule of maximum spin multiplicity.

Hund's Rule: Why Electrons Are Anti-Social

Imagine a classroom with four empty chairs arranged in a row. Students enter one by one. Do they all rush to sit next to each other, or does each student pick a separate chair first? Obviously, they spread out — each takes an empty chair before anyone has to share. Electrons in an atom behave the same way, and that's the heart of Hund's rule.

The Intuition: Minimising Repulsion

Electrons are negatively charged. They repel each other. If you force two electrons into the same orbital (the same "chair"), they have to occupy the same region of space — that's a lot of repulsion. It costs energy. So nature's first instinct is to keep them apart.

But there's a second, subtler reason. Electrons also behave like tiny magnets (they have "spin"). Two electrons with the same spin direction (both spinning clockwise, say) actually avoid each other due to a quantum mechanical effect — they can't be in the same place with the same spin. This further reduces repulsion. So parallel spins (same direction) are energetically favourable.

The Precise Statement

"Degenerate" just means same energy. The three $2p$ orbitals ($2p_x$, $2p_y$, $2p_z$) are degenerate. The five $3d$ orbitals are degenerate. Hund's rule governs how electrons fill these sets.

A Concrete Example: Nitrogen

Nitrogen has atomic number 7. Its electron configuration is $1s^2 2s^2 2p^3$. The $2p$ subshell has three orbitals and three electrons to place. Here's what happens:

• First electron goes into $2p_x$ (spin up, say).
• Second electron goes into $2p_y$ (spin up — parallel).
• Third electron goes into $2p_z$ (spin up — all three parallel).

No pairing occurs. All three electrons have the same spin. This is the maximum multiplicity — the maximum number of unpaired electrons possible.

What About Oxygen?

Oxygen has eight electrons: $1s^2 2s^2 2p^4$. Now we have four electrons for three $2p$ orbitals. Following Hund's rule:

• First three: one in each orbital, all spin up.
• Fourth electron: must pair up in one of the orbitals (say $2p_x$), with spin down.

So oxygen has two unpaired electrons (in $2p_y$ and $2p_z$), not four. The pairing happens only after every orbital has one electron. …