Question

Estimate the energy splitting between the lowest two levels for an electron in a three-dimensional

cube-shaped potential box with the side length 10 nm.

Answer 1

n=2

a=10nm

$E=\frac{n^2h^2}{8ma^2}$

$$E=\frac{2^2\times(6.625\times10^{-34})^2}{8\times9.1\times10^{-31}\times10^{-16}}=2.1\times10^{-21}J$$