Question

# Muons are unstable subatomic particles that decay with a mean lifetime of 2.197us (producing electrons and...

Muons are unstable subatomic particles that decay with a mean lifetime of 2.197us
(producing electrons and neutrinos) as measured in the inertial frame of the muons. Many
are produced in the upper atmosphere about 10 km above the surface of the Earth, and
some of them travel very near the speed of light on their way to the surface.

A) Calculate the largest distance any particle can travel in 2.197us, with both the time
and the distance measured by observers on the surface of the Earth. You will find a
distance much less than 10 km, so any muons that survive to reach the surface of the
Earth must live far longer than 2.197us as measured by an Earth observer. In fact,
most high-speed muons do survive the trip.

B) Consider muons traveling at a speed of 0.999 c relative to the Earth. Calculate the
average distance they travel toward the Earth before decaying as measured by an
Earth observer.

C) Consider muons traveling at a speed of 0.999 c relative to the Earth. Calculate the
thickness of the 10.0 km atmosphere as measured by observers in the muons' frame.

If you have any doubts, feel free to ask.

thank you :)

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