How thick is the atmosphere in the rest frame of a high-energy muon?

In summary, a muon with a mass of 106 MeV/c^2 and an energy of 10000 MeV is produced in the upper atmosphere, which is 100km thick. In the rest frame of the muon, the thickness of the atmosphere is 1.06km. The equation of relativity, specifically the gamma factor, can be used to calculate this. The speed of the muon is not needed.
  • #1
nn542
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Homework Statement


a muon(mass 106 MeV/c^2)is produced in the upper atmosphere with an energy of 10000MeV. The Earth's atmosphere is 100km thick.In the rest frame of the muon, how thick is the atmosphere?

Homework Equations



E^2=P^2c^2+m^2c^4(I don't know what equation to put here. I think I have to use the equation of relativity.)

The Attempt at a Solution


the answer is 1.06km

I'm wondering how to calculate the velocity of muon?~~
 
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  • #2
The thickness of the atmosphere has dimensions of what?
In relativity you get
1. time dilation
2. length contraction
... which do you think is needed here?

You don't need the speed of the muon, just the gamma factor.
Get it from the total energy: ##E=\gamma mc^2##
 

Related to How thick is the atmosphere in the rest frame of a high-energy muon?

1. What is special relativity with muon?

Special relativity with muon is a branch of physics that deals with the behavior of particles, specifically muons, at high speeds and in relation to the theory of special relativity proposed by Albert Einstein.

2. How does special relativity with muon differ from regular special relativity?

Special relativity with muon takes into account the fact that muons, unlike other particles, have a longer lifespan when they are moving at high speeds. This is due to time dilation, which is a key concept in special relativity.

3. What is the significance of studying special relativity with muon?

Studying special relativity with muon helps us better understand the fundamental laws of physics and how they apply to particles traveling at high speeds. It also has practical applications in fields such as particle accelerators and space travel.

4. How do we observe and measure special relativity with muon?

Scientists use particle accelerators to create high-speed muons and then observe their behavior using detectors. By measuring the decay rate of these muons, we can confirm the predictions of special relativity.

5. What are some real-world examples of special relativity with muon?

One notable example is the observation of muons in cosmic rays. These muons are traveling at speeds close to the speed of light, and their longer lifespan confirms the predictions of special relativity. Another example is in medical imaging, where the principles of special relativity are used to understand the behavior of particles in PET scans.

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