1.) What is the speed of a pion if its average lifetime is measured to be 4.20 ?

Question

1.) What is the speed of a pion if its average lifetime is measured to be 4.20 ? 10-8 s? At rest, its lifetime is 2.60 ? 10-8 s.

_______ c

2.) Particles called ?-mesons are created by accelerator beams. If these particles travel at 2.40 ? 108 m/s and live 2.60 ? 10-8 s when at rest relative to an observer, how long do they live as viewed in the laboratory?

____ s

3.) Particles called ?-mesons are created by accelerator beams. If these particles travel at 2.40 ? 108 m/s and live 2.60 ? 10-8 s when at rest relative to an observer, how long do they live as viewed in the laboratory?

____ s

4.) If relativistic effects are to be less than 8%, then ? must be less than 1.08. At what relative velocity is ? = 1.08?
____ c

Explanation / Answer

1.
t1/t2 = sqrt(1 - v^2 / c^2)
v = c sqrt(1 - (t1 / t2) ^2) =
= 0.785 c

2.
t1/t2 = sqrt(1 - v^2 / c^2)
t1/t2 = sqrt[1- (2.40 ? 108 )2/c2]
t2 = 4.33x10-8 s

3. Same question as Q2

4. gamma = sqrt{1/[1-(v2/c2)]}
1.08 = sqrt{1/[1-(v2/c2)]}
v = 0.377c

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