Answer
Electron speed is relativistic, so we calculated Lorentz factor:
$$\gamma=1+\frac{K}{m c^{2}}=1+\frac{2.5 \mathrm{MeV}}{0.511 \mathrm{MeV}}=5.892 $$
total energy carried by positron or electron is
$$E=\gamma m c^{2}=(5.892)(0.511 \mathrm{MeV})=3.011 \mathrm{MeV}=4.82 \times 10^{-13} \mathrm{J} $$
corresponding frequency of photons build is
$$f=\frac{E}{h}=\frac{4.82 \times 10^{-13} \mathrm{J}}{6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}}=7.3 \times 10^{20} \mathrm{Hz} $$
Work Step by Step
Electron speed is relativistic, so we calculated Lorentz factor:
$$\gamma=1+\frac{K}{m c^{2}}=1+\frac{2.5 \mathrm{MeV}}{0.511 \mathrm{MeV}}=5.892 $$
total energy carried by positron or electron is
$$E=\gamma m c^{2}=(5.892)(0.511 \mathrm{MeV})=3.011 \mathrm{MeV}=4.82 \times 10^{-13} \mathrm{J} $$
corresponding frequency of photons build is
$$f=\frac{E}{h}=\frac{4.82 \times 10^{-13} \mathrm{J}}{6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}}=7.3 \times 10^{20} \mathrm{Hz} $$
