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

Question

a) The average lifetime of a pi meson in its own frame of reference (i.e, the proper lifetime) is 2.60×10–8 s. If the meson moves with a speed of 0.980c, what is its mean lifetime as measured by an observer on Earth?

b) The average lifetime of a pi meson in its own frame of reference (i.e, the proper lifetime) is 2.60×10–8 s. If the meson moves with a speed of 0.980c, what is the average distance it travels before decaying, as measured by an observer on Earth?

Range of answers: 18.7 m to 56.2 m

c) The average lifetime of a pi meson in its own frame of reference (i.e, the proper lifetime) is 2.60×10–8 s. If the meson moves with a speed of 0.980c, what distance would it travel if time dilation did not occur?

Range of answers: 7.15 m to 7.90 m

Explanation / Answer

a)

Average life time of pi-meson, t = 2.60 x 10^-8 s

speed of the pi-meson, v = 0.980c

time dialation is

t' = t / sqrt(1 - v^2/c^2)

t' = (2.6 x 10^-8) / sqrt(1 - 0.980c^2/c^2)

t' = 13.1 x 10^-8 sec

b)

Average distance measured by observer,

d = v'*t

d = 0.980*c x 13.1 x 10^-8

d = 0.980 x 3 x 10^8 x 13.1 x 10^-8

d = 38.514 m

c)

If time dialation not occure distaance travel is

d = v*t

d = 0.980 x 3 x 10^8 x 2.6 x 10^-8

d = 7.644 m

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