# Muon beam intensity and distance

• Ayame17
In summary, the conversation discussed the question of how far a beam of muons with different kinetic energy levels would travel in empty space before its intensity is reduced by half. The relevant equations for this problem were discussed, including the use of half life and time dilation. The conversation also addressed the calculation of speed from the gamma factor and the importance of taking into account the time dilation for higher energy beams. Finally, it was mentioned that the half-life of the muon had already been given and that the calculation of speed from gamma was necessary. Overall, the conversation provided helpful information for solving the given problem.
Ayame17

## Homework Statement

How far will a beam of muons with kinetic energy (a) 1 MeV, (b) 100 GeV travel in empty space before its intensity is reduced by half?

See below

## The Attempt at a Solution

My main problem with this is that it looks like we won't be taught the relevant material until the day before the work is due in. I could wait, but I'd rather get it sorted beforehand. I'm not asking for the answer, but if someone could give me some kind of relevant equation to get started, I would be very grateful!

Use half life and time dilation.

Where does the intensity come into it though?

intensity is number of particles per area, so what is reducing the intensity is the decay of the particles.

Ah, I see...you work out gamma via $$E=\gamma*mc^{2}$$...since you need the speed to calculate the distance, I'm assuming you calculate the speed from the gamma factor...it certainly seems to work okay.

Yes, that is correct. Also take into account the time dilation, the higher energy the beam has, the longer life time the particles will have in the frame in which they are traveling in.

The life time of the muon is 2.2 micro seconds, and is the time it gets for a sample of particles to be reduced by the factor of 1/e. So you need to find the "half life" of the muon.

Thankfully we'd already been given the half-life, and we figured we'd have to calculate the speed from gamma...thanks for verifying, you've been a great help!

Ok, great. good luck then.

## 1. What is a muon beam?

A muon beam is a concentrated stream of muons, which are subatomic particles that are similar to electrons, but with a higher mass. Muons are created in the upper atmosphere by cosmic rays and can be produced artificially in particle accelerators.

## 2. How is muon beam intensity measured?

Muon beam intensity is typically measured by counting the number of muons passing through a specific area in a given amount of time. This can be done using detectors or specialized equipment such as scintillators. The intensity can also be calculated by measuring the energy and velocity of the muons.

## 3. What factors affect muon beam intensity?

Muon beam intensity can be affected by various factors, including the energy and velocity of the muons, the distance they travel, and any obstructions or interactions they encounter along their path. Additionally, the production and collection methods used in creating the muon beam can also impact its intensity.

## 4. How does distance affect muon beam intensity?

The intensity of a muon beam decreases as the distance from its source increases. This is due to factors such as the scattering and absorption of muons as they travel through a medium, as well as the natural decay of muons over time.

## 5. How is muon beam intensity used in scientific research?

Muon beam intensity is used in a variety of scientific research fields, including particle physics, materials science, and geophysics. Muon beams can be used to study the structure of materials and molecules, investigate subatomic particles and their interactions, and even probe geological formations deep underground. By measuring the intensity of muons, scientists can gain valuable insights into the properties and behavior of matter at the atomic and subatomic level.

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