Chapter 31, Problem 1OQ

To determine

The total kinetic energy of the particles.

Answer to Problem 1OQ

Option (c).

Explanation of Solution

In the given decay process, muon decays into an electron, electron antineutrino and a muon neutrino. Here, muon is having greater value of rest mass energy than electron and neutrinos together.

The rest mass energy for muon is 105.7MeV/c². On the other hand, the electron is having rest mass energy for 0.511MeV/c² and that for neutrinos is less than 0.3MeV/c². Thus, muon is having more rest mass energy than others.

Write the expression for the energy.

$m_{\mu }{c}^2=K_{tot}+m_e{c}^2+m_{{\overline{\nu }}_e}{c}^2+m_{{\tau }_{\tau }}{c}^2$

Here, $m_{\mu }$ is the mass of muon, $m_{{\tau }_{\tau }}$ is mass muon neutrino, $m_{{\overline{\nu }}_e{}_e}$ is the mass of electron antineutrino, $m_e$ is the mass of electron, $c$ is the speed of light and $K_{tot}$ is the total kinetic energy.

Conclusion:

Since, the muon is having more rest mass energy than others. Thus, option (c) is correct.

Since, total kinetic energy is not zero. Thus, option (a) is incorrect.

Since, the muon is not having less rest mass energy than others. Thus, option (b) is incorrect.

Since, the muon is having more rest mass energy than others. Thus, option (d) is incorrect.