The average lifetime of a pi meson in its own frame of reference (i.e., the prop

Question

The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10 - 8 s. If the meson moves with a speed of 0.90c, what is its mean lifetime as measured by an observer on Earth? Regard the pi meson as a clock measuring its lifetime in its own rest frame. What time interval does this lifetime become in a reference frame in which the pi meson is moving at the specified speed? S What is the average distance it travels before decaying, as measured by an observer on Earth? What distance would it travel if time dilation did not occur?

Explanation / Answer

a)

t' = t/(1-v^2/c^2) = 2.6*10^-8/(1-0.9^2) = 1.37*10^-7 s

b)

d = v*t' = 0.9*3*10^8*1.37*10^-7 = 36.99 m

c)

d' = v*t = 0.9*3*10^8*2.6*10^-8 = 7.02 m

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