Answer
$\lambda = 1.84\times 10^{-14}~m$
Note that each gamma ray must have the same wavelength as they must have the same momentum when they are sent of in opposite directions, which conserves the momentum of zero.
Work Step by Step
The $\pi^0$ has rest energy $135.0~MeV$
Then each gamma ray must have energy $\frac{135.0~MeV}{2} = 67.5~MeV$
We can find the wavelength of each gamma ray:
$\lambda = \frac{h~c}{E}$
$\lambda = \frac{(6.626\times 10^{-34}~J~s)~(3.0\times 10^8~m/s)}{(67.5\times 10^6~eV)(1.6\times 10^{-19}~J/eV)}$
$\lambda = 1.84\times 10^{-14}~m$
Note that each gamma ray must have the same wavelength as they must have the same momentum when they are sent of in opposite directions, which conserves the momentum of zero.
