Answer
$1.32\times10^{-15}m$
Work Step by Step
The combined mass energy of the proton and antiproton transforms into the energy of the two photons.
Assume the photons have equal energy so that momentum is conserved.
$$2mc^2=2hf=2h\frac{c}{\lambda}$$
$$\lambda=\frac{hc}{mc^2}$$
$$=\frac{(6.63\times10^{-34} J \cdot s)(3.00\times10^8m/s)}{(938.3\times10^{6}eV)(1.60\times10^{-19}J/eV)}$$
$$=1.32\times10^{-15}m$$
