The proper mean lifetime of a sub-nuclear particle, called a muon, is 2 µs. Muon
ID: 2025425 • Letter: T
Question
The proper mean lifetime of a sub-nuclear particle, called a muon, is 2 µs. Muons in a beam are traveling at 0.982 c relative to a laboratory. The speed of light is 2.998 × 10^8 m/s.In the reference frame of the muon, how far does the laboratory travel in a typical lifetime of 2 µs?
Answer in units of m.
What is this distance in the laboratory’s frame?
Answer in units of km.
I've tried to use the 1/sqrt(v^2/C^2) equation, but Can't get the right answer. Please show all the steps so I can do this on other problems.
Thanks!
Explanation / Answer
proper mean lifetime of a sub-nuclear particle, called a muon is ,t = 2 µs Muons in a beam are traveling at a speed , v = 0.982 c (relative to a laboratory) Here , c is the speed of the light = 2.998 × 108 m/s(I) In the reference frame of the muon, how far does the laboratory travel in a typical lifetime of 2 µs is d = v t = (0.982c)(2s) = (0.982 x2.998 x 108 m/s)(2x10-6s) = 588.8 m (II) Acc.to special theory of relativity when the muon travels with a speed comparable to speed of the light , the profer meantime of the muon is when measured from laboratory frame is given by the formula t' = t / [1-v2/c2] = (2 µs ) / [1-(0.982 c)2/c2] = 10.58 µs thus, distance in the laboratory’s frame is d' = v t' = (0.982 x2.998 x 108 m/s)(10.58x10-6s) = 3.114 Km (II) Acc.to special theory of relativity when the muon travels with a speed comparable to speed of the light , the profer meantime of the muon is when measured from laboratory frame is given by the formula t' = t / [1-v2/c2] = (2 µs ) / [1-(0.982 c)2/c2] = 10.58 µs thus, distance in the laboratory’s frame is d' = v t' = (0.982 x2.998 x 108 m/s)(10.58x10-6s) = 3.114 Km
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