Question

The average lifetime of muons at rest is 2.20 us. A laboratory measurement on muons traveling in a beam emerging from a particle accelerator yields an average muon lifetime of 19.668 us. What is the speed of the muons in the laboratory?
u=((1-(2.2e-6/19.688e-6)^2))^(1/2)=0.994c=2.98e8 m/s

ok I've got this part but I'm having trouble with these parts of the problem

B.What is their kinetic energy? (MeV)

C.What is their momentum? (MeV/c - Do not enter a unit) The mass of a muon is 207 times that of an electron.

Answer 1

The ratio by which the apparent lifetime is lengthened, 8.94, equals the "gamma" factor,
1/sqrt[1 - (v/c)^2]

Solve for v/c

b. The kinetic energy (in Joules) is
(gamma-1)*Mo*c^2 = 7.94 Mo c^2
where Mo is the rest mass of the mu-meson. You will have to convert that to MeV.

1 MeV = 1.6*10^-12 J

c. The momentum is gamma*Mo*v.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

You will have to convert that to MeV/c

1 MeV/c = 5.33*10^-21 kg m/s

Answer 2

drwls you are awesome!!