Answer
77.5 nm.
Work Step by Step
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 second excited level has n = 3.
$\Delta E = E_3-E_1=\frac{3^2 h^2}{8mL^2}-\frac{1^2 h^2}{8mL^2}=8E_1$
We are told that this energy difference is $ 8E_1=16.0 eV $. Solve for the wavelength.
$$\lambda =\frac{hc}{\Delta E}=\frac{1.24\times10^{-6}eV\cdot m}{16.0eV}=7.75\times10^{-8}m$$
