Chapter 32, Problem 27P

To determine

The maximum kinetic energy of the electron when muon decays from rest via

${\mu }^{-}\to e^{-}+{\overline{V}}_c+V_{\mu }$

Answer to Problem 27P

Solution:

The maximum kinetic energy of the electron when muon decays from the r4est ${\mu }^{-}\to e^{-}+{\overline{V}}_c+V_{\mu }$ is $52.34MeV$.

Explanation of Solution

Given info.:

${\mu }^{-}\to e^{-}+{\overline{V}}_c+V_{\mu }$

Formula used:

$K.E=\frac{Q^2}{2m_{{\mu }^{-}}{c}^2}$

Calculation:

The Q-value of reaction can be calculated as

$\begin{array}{c}Q=\left[m_{{\mu }^{-}}-m_{e^{-}}\right]c^2\\ =m_{{\mu }^{-}}{c}^2-m_{e^{-}}{c}^2\end{array}$

Substitute $m_{{\mu }^{-}}{c}^2=105.7MeV,m_{e^{-}}{c}^2=0.511MeV$

$\begin{array}{c}Q=\left(105.7-0.511\right)MeV\\ =105.189MeV\\ K.E.=\frac{{\left(105.189\right)}^2}{2\times 105.7}\\ =\frac{11064.72572}{211.4}\\ =52.34MeV\end{array}$

Therefore, the maximum kinetic energy is $52.34MeV$.