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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 = Dto/(1 - v2/c2)1/2 Dt = 2.2 x 10-6/(1 - 0.62)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 = Dto /(1 – v2/c2)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 – 0.6c2/c2)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.

 
 
 
© Keith Gibbs 2013