CHEM 121 glossary

Particle in a box

A model of a particle moving freely along a line of length $L$ between infinitely high walls. Only standing waves that fit a whole number of half-wavelengths are allowed, giving $E_n = \dfrac{n^2h^2}{8mL^2}$ with $n = 1, 2, 3, \ldots$

$\psi_2$ : two half-wavelengths fit in the box, with one node at the centre.

Example

Butadiene's π electrons are modelled in a box of $L = 4 \times 0.140 = 0.560$ nm, so $E_1 = 1.92\times10^{-19}$ J. The $n = 2 \to 3$ gap is $5E_1 = 9.61\times10^{-19}$ J, an absorption near 207 nm.