CHEM 121 glossary

Quantization

The restriction of a quantity, such as the energy of a bound particle, to certain separate allowed values rather than any value. Confinement causes quantization: a free particle can have any energy, but one trapped in a box or an atom cannot.

Particle in a box: only the energies $E_n = n^2E_1$ are allowed.

Example

A hydrogen atom can have $E = -2.179\times10^{-18}$ J ( $n = 1$ ) or $-5.45\times10^{-19}$ J ( $n = 2$ ), but nothing in between, which is why its spectrum has sharp lines.