# Electron spin and the Pauli principle

> Why paired electrons cancel and unpaired ones don't


## Objectives

- Explain that a spinning electron behaves like a tiny magnet, and that $\uparrow$ and $\downarrow$ show its two spin directions.
- State the Pauli exclusion principle for one orbital: two electrons at most, with opposite spins ($\uparrow\downarrow$).
- Explain why the magnetic effects of two paired electrons cancel, while an unpaired electron keeps its effect.

## 1. Electron spin and the Pauli principle: from zero




## 2. Two tiny magnets in one box

Predict: two electrons share one orbital. What happens to their magnetic effects?

- They cancel, because the two electrons spin in opposite directions ✓
- One of the electrons stops spinning
- They add up, so the orbital is twice as magnetic

The two electrons in one orbital spin in opposite directions, so their magnetic effects cancel. This is what the Pauli exclusion principle requires.

[ar-EG] الـ electrons الاتنين اللي في orbital واحد بيعملوا spin في اتجاهين عكس بعض، فالتأثير المغناطيسي بتاعهم بيلغي بعضه. وده اللي الـ Pauli exclusion principle بيطلبه.
## 3. Spin makes a tiny magnet

Remember: an orbital is the region around the nucleus where an electron is most likely found. spin Each electron spins around its own axis. This spinning forms a magnetic field, so the electron behaves like a tiny magnet. One electron: the arrow shows its spin direction An electron can spin in one of two directions. We draw them as $\uparrow$ and $\downarrow$. An electron drawn as $\downarrow$ is a negative or missing electron.


## 4. The Pauli exclusion principle

Pauli exclusion principle One orbital holds two electrons at most, and they must have opposite spins ($\uparrow\downarrow$). $\uparrow\downarrow$: a pair with opposite spins With opposite spins, the two tiny magnets point opposite ways. So their magnetic effects cancel.


## 5. Paired or unpaired?

Add electrons to one orbital and watch what happens. Electrons added An empty orbital $\uparrow$: one **unpaired** electron. Its magnetic effect is not cancelled. $\uparrow\downarrow$: a **pair**. The two magnetic effects cancel. The third electron can't join the pair. It goes to another orbital. Not allowed in the same orbital: Pauli allows two electrons at most. unpaired electron An electron alone in its orbital ($\uparrow$). Its magnetic effect is not cancelled.


## 6. Check yourself

Which orbital breaks the Pauli exclusion principle?

- $[\uparrow]$
- $[\uparrow\uparrow]$ ✓
- $[\uparrow\downarrow]$

$[\uparrow\uparrow]$ breaks the Pauli exclusion principle: two electrons in one orbital must have opposite spins. $[\uparrow\downarrow]$ follows it, and one unpaired electron, $[\uparrow]$, breaks no rule.

[ar-EG] الـ $[\uparrow\uparrow]$ هو اللي بيكسر الـ Pauli exclusion principle: اتنين electrons في orbital واحد لازم يكون ليهم opposite spins. الـ $[\uparrow\downarrow]$ ماشي عليه، والـ unpaired electron الواحد، $[\uparrow]$، مش بيكسر أي قاعدة.
## 7. Summary

A spinning electron behaves like a tiny magnet. $\uparrow$ and $\downarrow$ are its two spin directions. Pauli: one orbital holds two electrons at most, with opposite spins ($\uparrow\downarrow$). A pair's magnetic effects cancel. An **unpaired electron** keeps its effect. Book wording you'll meet Unpaired electrons ($\uparrow$) form a magnetic field **due to their spinning**. Magnetic properties of transition elements, in Chapter 1. Can you explain why two electrons in the same orbital have no overall magnetic effect? The two electrons have opposite spins ($\uparrow\downarrow$). Their two tiny magnets point opposite ways, so their magnetic effects cancel.



Chapter: Transition Elements (https://yaani.ai/en/learn/chemistry/chem-s3-en.ch1)
Source: https://yaani.ai/en/lesson/chem-s3-en.lesson-atom.electron-spin-pauli