Question

A muon is traveling at 0.981

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

Answer 1

The rest mass of the muon is 207 times the mass of the electron:

`m=207 m_e = 207 \cdot 9.1 \cdot 10^(-31) kg = 1.88 \cdot 10^(-28)kg`

The relativistic momentum of a particle is given by

`p= \gamma m v`
where
m is the particle's mass
v is its velocity

`\gamma = \frac{1}{ \sqrt{1- (v^2)/(c^2) } }` is the relativistic factor, with c being the speed of light.

The muon is traveling at speed
`v=0.981 c`, so the relativistic factor is

`\gamma = \frac{1}{ \sqrt{1- ((0.981 c)/(c))^2 } } =5.154`

So the momentum of the muon is

`p= \gamma m v = (5.154)(1.88 \cdot 10^(-28)kg)(0.981 \cdot (3 \cdot 10^8 m/s))=`

`=2.85 \cdot 10^(-19) kg m/s`