Daily Physicist

Today is the birthday of

• Otto Stern (1888-1969).

Today’s Problem

A typical fission produced gamma ray has a frequency of \(10^{20}\) Hz. How many of these gamma ray photons does it take to equal the rest mass energy of an electron?

Answer

The energy of a gamma ray photon given its frequency \(\nu\) is \(E=h\nu\) where \(h\) is Planck’s constant (\(6.626\times 10^{-34}\,\text{J}\cdot\text{s}\)). The rest mass energy of an electron is \(E=m_{e}c^2\). So we want to solve for the integer \(n\) in the equation \(nh\nu = m_ec^2\). Solving for \(n\) we get

\[n=\frac{m_ec^2}{h\nu}=\frac{(9.109\times 10^{-31}\,\text{kg})(2.998\times 10^{8}\text{m/s})^2}{(6.626\times 10^{-34}\,\text{J}\cdot\text{s})(10^{20}\,\text{s}^{-1})}=1.236\]

So the energy of a fission produced gamma ray is on the order of the rest mass energy of one electron.