# Uncertainty principle

You cannot know both a particle's position and momentum exactly: change in x times change in p is at least h-bar / 2.

Physics (university) · Part 10: Relativity and quantum physics · Card 8 of 11 · Last updated 2026-10-19

## Analogy

Squeezing a balloon in one place makes it bulge elsewhere.

## Example

**Confined electron**

dp >= 1.05e-34 / (2 x 1e-10)
= 5.3e-25
dv = 5.8e5 m/s

## In practice

Squeezing an electron into 1e-10 m means its speed is uncertain by about 6e5 m/s.

## Practice

### Flashcards

- **State the uncertainty principle.** Position and momentum cannot both be known exactly: dx dp is at least h-bar/2.

## Questions people ask

### Is uncertainty caused by bad measuring tools?

No. It is a basic property of nature. A particle does not have a precisely defined position and momentum at once. Better instruments cannot beat the limit, because a wave can only be sharply localised in space by mixing together many wavelengths, which spreads out its momentum.

### Why do atoms not collapse?

If an electron fell into the nucleus, its position would be known very precisely, so its momentum and energy would be huge and uncertain. The balance between pulling inward and the cost of squeezing sets the size of an atom, about 1e-10 m.

## Related concepts

- [Photon](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-5)
- [Photoelectric effect](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-6)
- [de Broglie wavelength](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-7)
- [Wave function](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-9)

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