Question

Calculate the difference in mass, in kilograms, between the muon and pion of Sample Problem 44.01.

Short answer

The difference in mass between the pion and muon is $6.03\times {10}^{-29}\mathrm{kg}$.

Step-by-step solution

Given data

The interaction provided is

${\mathrm{\pi }}^{+}\to {\mathrm{\mu }}^{+}+\mathrm{\nu }$

Rest mass of muon and pion

The muon rest mass is

${\mathrm{m}}_{0\mathrm{\mu }}=105.7\mathrm{MeV}/{\mathrm{c}}^2.......1$

The pion rest mass is

role="math" localid="1663137427708" ${\mathrm{m}}_{0\mathrm{\pi }}=139.6\mathrm{MeV}/{\mathrm{c}}^2........2$

Here, c is the speed of light in vacuum with value

$\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}$

Determining the difference in masses of muon and pion

From equations (I) and (II), the difference in the masses of muon and pion are

$$\begin{gathered} {\mathrm{m}}_{0\mathrm{\pi }}-{\mathrm{m}}_{0\mathrm{\mu }}=139.6{\text{MeV/c}}^{\text{2}}-105.7{\text{MeV/c}}^{\text{2}} \\ =\frac{33.9}{{\left(3\times {10}^8\right)}^2}·\left(1\text{MeV}\times \frac{1.602\times {10}^{-13}\text{kg}·{\text{m}}^2{\text{/s}}^{\text{2}}}{1\text{MeV}}\right)·\left(\frac{1}{1{\text{m}}^2{\text{/s}}^{\text{2}}}\right) \\ =6.03\times {10}^{-29}\text{kg} \end{gathered}$$

Thus, the difference is $=6.03\times {10}^{-29}\text{kg}$.