Question

A muon is traveling at 0.988

c. what is its momentum? (the mass of such a muon at rest in the laboratory is 207 times the electron mass.)

Answer 1

As per Einstein's relation of relativity

`m = \frac{m_0}{\sqrt{1 - (v^2)/(c^2)}}`

here we know that

`m_0 = 207 m_e = 207 * 9.11 * 10^(-31) kg`

`m_0 = 1.88 * 10^(-28) kg`

now here we know that

`v = 0.988 c`

now from above equation mass of the muon is given as

`m = (1.88 * 10^(-28))/(√(1 - 0.988^2))`

`m = 1.22 * 10^(-27) kg`

now for the momentum of muon we can use

`P = mv`

`P = 1.22 * 10^(-27) * 0.988(3 * 10^8)`

`P = 3.62 * 10^(-19) kg m/s`

so above is the momentum of muon