Answer
$\lambda = 2.4\times 10^{-12}~m$
Work Step by Step
An electron and a positron each have a rest energy of $0.511~MeV$
We can find the wavelength of each photon produced by the annihilation:
$E = \frac{hc}{\lambda}$
$\lambda = \frac{hc}{E}$
$\lambda = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{(0.511\times 10^6~eV)(1.6\times 10^{-19}~J/eV)}$
$\lambda = 2.4\times 10^{-12}~m$
