Answer
$10\;\mu m$
Work Step by Step
The lasing action occurs when the electrons jump from the energy level $E_2$ to energy level $E_1$.
Thus, the energy associated with the laser is:
$ \Delta E=E_2-E_1=(0.289-0.165)\;eV=0.124\;eV$
Therefore, the wavelength of laser is
$\lambda=\frac{ch}{\Delta E}$
or, $\lambda=\frac{1240\;eV-nm}{\Delta E \;(eV)}$
or, $\lambda=\frac{1240\;eV-nm}{0.124 \;eV}$
or, $\lambda=1.0\times10^{3}\;nm$
or, $\lambda=10\;\mu m$
