Answer
$\lambda = 1.10\times 10^{-6}~m$
Work Step by Step
We can find the energy of the radiation that is emitted:
$E = E_6-E_3$
$E = \frac{E_0}{6^2}-\frac{E_0}{3^2}$
$E = E_0~(\frac{1}{6^2}-\frac{1}{3^2})$
$E = (-13.6~eV)~(-\frac{1}{12})$
$E = 1.13~eV$
We can find the wavelength of the radiation:
$E = \frac{hc}{\lambda}$
$\lambda = \frac{hc}{E}$
$\lambda = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{(1.13~eV)(1.6\times 10^{-19}~J/eV)}$
$\lambda = 1.10\times 10^{-6}~m$
