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# speed of muons

Mon 29 Sep, 2014 10:39 am
A certain muon detector counts 600 muouns / h at an altitude of 1900m and 380 / h at sea level. Given that the muon half-life at rest is 1.5 × ( 10^-6)s, determine the speed of the muons relative to Earth, assuming that they all have the same speed.
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Lordyaswas

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Mon 29 Sep, 2014 12:11 pm
@htbowser,
I think everyone would like to jump in, but like me, they are probably asking themselves the same question.

OK, I will therefore get the ball rolling and ask.

Are we talking a standard size muon here? Around about 200 times the size of an electron?
contrex

1
Mon 29 Sep, 2014 01:00 pm
A person with variations of the name htbowser has been asking this all over the web. This is an arithmetic question, to do with time dilation. High-energy cosmic ray protons entering the upper atmosphere interact with the nuclei of oxygen and nitrogen atoms to give a group of pions and these then decay into muons that then move off at a speed of up to 0.994 c. These muons are formed at a height of between ten and fifteen thousand metres above the ground.

The half-life of a muon is 2.2 microseconds and so even moving at 0.994 c they would only expect to travel about 660 m before half of them decayed. Muons formed at, say 12000 m would take 40 <μs or about 20 half lives to reach the ground. This would mean that only 1/220 of the original number would be detected. The fact that the proportion is much higher than this means that the muons are living longer.

The exact same question was asked on Physics Stack Exchange about 3 hours ago and was locked because:

Quote:
Homework-like questions should ask about a specific physics concept and show some effort to work through the problem.

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thack45

1
Mon 29 Sep, 2014 05:35 pm
@Lordyaswas,
It's like you're in my head!
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izzythepush

1
Wed 1 Oct, 2014 08:41 am
When I spent a week in the country there was a cow in the next field that would moo on and on and on. I never realised it was a physicist.
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