Answer
260 MeV
Work Step by Step
The muons’ total energy (rest energy plus kinetic energy) becomes electromagnetic energy.
Use equation 26–6b.
$$E_{photon}=E_1+E_2=\gamma_1mc^2+\gamma_2mc^2=(\gamma_1+\gamma_2)mc^2$$
$$ =(\frac{1}{\sqrt{1-0.53^2}}+\frac{1}{\sqrt{1-0.65^2}})(105.7MeV)$$
$$ =263.7MeV\approx260MeV$$