Answer
$1.3\times10^{-12}m$
Work Step by Step
The energies of the electron and positron transform into the energy of the 2 photons. Assume the photons have equal energy so that momentum is conserved.
$$2(mc^2+KE)=2hf=2h\frac{c}{\lambda}$$
$$\lambda=\frac{hc}{mc^2+KE}$$
$$=\frac{(6.63\times10^{-34} J \cdot s)(3.00\times10^8m/s)}{((511+420)\times10^{3}eV)(1.60\times10^{-19}J/eV)}$$
$$=1.3\times10^{-12}m$$
