Question

A muon is traveling at 0.988

Answer 1

As per Einstein's relation of relativity

$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$

here we know that

$m_0 = 207 m_e = 207 \times 9.11 \times 10^{-31} kg$

$m_0 = 1.88 \times 10^{-28} kg$

now here we know that

$v = 0.988 c$

now from above equation mass of the muon is given as

$m = \frac{1.88 \times 10^{-28}}{\sqrt{1 - 0.988^2}}$

$m = 1.22 \times 10^{-27} kg$

now for the momentum of muon we can use

$P = mv$

$P = 1.22 \times 10^{-27} \times 0.988(3 \times 10^8)$

$P = 3.62 \times 10^{-19} kg m/s$

so above is the momentum of muon