Answer
111 nm.
Work Step by Step
The energy levels are given by $E_n=(n+\frac{1}{2})\hbar\omega$.
The ground state energy is when n=0.
The energy difference between any two states is 11.2 eV, which is twice the ground state energy of 5.60 eV.
Find the wavelength.
$$\lambda =\frac{hc}{\Delta E}$$
$$\lambda =\frac{1.24\times10^{-6}eV\cdot m}{11.2eV }=1.11\times10^{-7}m $$
