Answer
$\lambda=6.67943\times10^{-12}m$
Work Step by Step
Energy of $\gamma$ ray photon is $E= 0.186MeV=0.186\times10^{6}eV$
$1eV$ is equal to $1.6\times10^{-19}J $
so $0.186\times10^{6}eV$ is equal to $0.186\times10^{6}\times 1.6\times10^{-19}J $
$E=0.2976\times10^{-13}J$
From Plank's hypothesis
$E=hf=\frac{hc}{\lambda}$
$\lambda=\frac{hc}{E}$
putting the values of
$h=6.626\times10^{-34}J.s$,
$E=0.2976\times10^{-13}J$,,
$c=3\times10^{8}m/s$
$\lambda=\frac{6.626\times10^{-34}J.s\times 3\times10^{8}m/s}{0.2976\times10^{-13}J}$
$\lambda=66.7943\times10^{-13}m$
$\lambda=6.67943\times10^{-12}m$
