CHEM 121 glossary

Heisenberg uncertainty principle

The position and momentum of a particle cannot both be known exactly at once: $\Delta x\,\Delta p \ge h/4\pi$ . It is a property of nature, not of our instruments, and it is why an electron in an atom has no definite path.

Example

If an electron's speed is known to within $\Delta v = 1.0\times10^{3}$ m/s, its position is uncertain by at least $\Delta x = \dfrac{6.626\times10^{-34}}{4\pi(9.109\times10^{-31})(1.0\times10^{3})} = 5.8\times10^{-8}$ m, about 58 nm.