Question

The \[{{\rm{\pi }}^{\rm{0}}}\]is its own antiparticle and decays in the following manner: \[{\pi ^0} \to \gamma + \gamma \]. What is the energy of each \[\gamma \]ray if the \[{\pi ^0}\] is at rest when it decays?

Short answer

The energy of each \[\gamma \] ray if the \[{\pi ^0}\], at rest, decays is \[67.5\;{\rm{MeV}}\].

Step-by-step solution

Definition of Energy

According to the law of energy conservation, the energy content of the universe always remains conserved. The unit of energy for CGS is erg, and the unit of energy for SI is joule.

Given Data

\({\pi ^o}\)decays in the following manner-\[{\pi ^0} \to \gamma + \gamma \]

Finding required energy

The\[{\pi ^0}\]is at rest, the only energy it possesses is its mass\[\left( {m{c^2}} \right)\].the energy is divided between the two\[\gamma \]rays equally. So, energy of each ray is-

\[\begin{array}{c}{E_\gamma } = \frac{{{E_{{\pi ^0}}}}}{2}\\ = \frac{{135\;{\rm{MeV}}}}{2}\\ = 67.5\;{\rm{MeV}}\end{array}\]

The energy of each \[\gamma \] ray when \[{\pi ^0}\] decays is \[67.5\;{\rm{MeV}}\].