## University Physics with Modern Physics (14th Edition)

$6.1\times10^{-10}m$.
The energy levels in a 1D box are given by the equation $E_n=\frac{n^2 h^2}{8mL^2}$. The ground state has n=1, and the first excited level has n = 2. $\Delta E = E_2-E_1=\frac{2^2 h^2}{8mL^2}-\frac{1^2 h^2}{8mL^2}=\frac{3 h^2}{8mL^2}$ We are told that this energy difference is $3.0 eV=4.8\times10^{-19}J$. Solve for L. $$L=h\frac{\sqrt{3}}{\sqrt{8m \Delta E}}=6.1\times10^{-10}m$$