Muon lifetime
QUESTION:
The proper lifetime of a muon is 2.2 x 10
-6 s. Muons in a beam are moving with
speed 0.6c relative to an inertial observer. How far will a muon in the beam travel before it
decays?
Dt =
Dt
o/(1 - v
2/c
2)
1/2
Dt = 2.2 x 10
-6/(1 - 0.6
2)
1/2
Dt = 2.75 x 10
-6 s
Answer:
The time for a muon moving at high speed runs more slowly than
that for a stationary observer and so:
Dt =
Dt
o /(1 – v
2/c
2)
1/2 the
formula that you have quoted.
(Actually you typed the wrong formula with the
numbers missing out the squares but you have actually used it correctly to get the answer for
delta t.)
Substituting the numbers given:
Dt =
2.2 x 10
-6 /(1 – 0.6c
2/c
2)
1/2 = 2.2x10
-6 x
1.25 = 2.75 x 10
-6 s
Therefore distance travelled = 0.6c x 2.75 x 10
-
6 m = 495 m (500 m to a reasonable accuracy).
An inertial observer is one that
moves at a constant velocity relative to another reference frame.
