Chapter 27, Problem 35P

To determine

The minimum photon energy needed to produce ${\mu }^{+}{\mu }^{-}$ pair and wavelength of such photon.

Answer to Problem 35P

Solution:

• The minimum photon energy needed to produce ${\mu }^{+}{\mu }^{-}$ pair is $212\text{MeV}$.

• Wavelength of such a photon is $5.85\times {10}^{-15}\text{m}$.

Explanation of Solution

Given:

Mass of each $\mu$: 207 times of mass of electron.

Formula Used:

$hf=\frac{hc}{\lambda }=2m_0{c}^2$

Calculation:

The minimum photon energy needed can be given by the below formula

$\begin{array}{c}E=2m_0{c}^2\\ =2\times (207)\times (0.511\text{MeV)}\\ \text{=211}\text{.554}\text{MeV}\approx \text{212}\text{MeV}\end{array}$

The wavelength of the photon can be given as

$\begin{array}{l}E=\frac{hc}{\lambda }\\ \text{or,}\lambda \text{=}\frac{hc}{E}=\frac{4.1357\times {10}^{-15}\text{eV}\text{s}\times 3\times {10}^8\text{m/s}}{212\times {10}^6\text{eV}}=5.85\times {10}^{-15}\text{m}\end{array}$