# Particle Accelerator problem with a proton beam hitting a target

• OmegaFury
In summary, the current in a particle accelerator carries a proton beam with a radius of 1.30 mm. If the beam hits a target, 5.625 x 1015 protons hit the target in 3s.
OmegaFury

## Homework Statement

In a certain particle accelerator, a current of 300μA is carried by a 4.00-MeV proton beam that has a radius of 1.30 mm. The mass of a proton is 1.67 x 10-27kg. If the beam hits a target, how many protons hit the target in 3s?

## Homework Equations

The only equation that even remotely comes to mind regarding this problem is I=e2n(tau)AE/me

I do not know which variable has the electron volt unit, or an equation involving current and time.

## The Attempt at a Solution

I don't even know where to begin as I don't know a suitable formula to solve the problem. Perhaps if I knew that, I could get somewhere.
--Also, for personal curiosity-- In the formula for current that I listed, what exactly is tau?
Also, is n the number of particles, or the number density? And is E the electric field? My book didn't exactly break the formula down as well as I'd like.

Last edited:
If you don't know what the formula means then it's useless. What does an ampere (the A in your formula) mean? I think they gave you a lot of numbers in that problem that don't really matter. Try to understand what an ampere is first.

Okay. Well. An ampere is equal to 1C/1s. So I guess that is where the time would come in. 300μA= 300 x 10-6A = 300 x 10-6C/S. So would I just multiply that by 3s to cancel the seconds, leaving only coulombs? Then divide by 1.60 x 10-19C (I suppose that would be the charge of one proton). Which would equal 5.625 x 1015 protons.

I highly doubt this is the case because I'm sure the radius has some influence on how many protons hit the target.

Last edited:
OmegaFury said:
Okay. Well. An ampere is equal to 1C/1s. So I guess that is where the time would come in. 300μA= 300 x 10-6A = 300 x 10-6C/S. So would I just multiply that by 3s to cancel the seconds, leaving only coulombs? Then divide by 1.60 x 10-19C (I suppose that would be the charge of one proton). Which would equal 5.625 x 1015 protons.

I highly doubt this is the case because I'm sure the radius has some influence on how many protons hit the target.

But they don't give you the target size, do they? How can you use the beam radius?

I'm assuming that the target is two-dimensional and is as big as the cross-sectional area of the beam.

OmegaFury said:
I'm assuming that the target is two-dimensional and is as big as the cross-sectional area of the beam.

So am I. So the whole beam hits the target. So how can changing the radius change the number of particles hitting the target?

Oh. I think I see what you're getting at. Electric current already incorporates the cross-sectional area as part of the equation. When calculating for the number of protons, you do calculate for the total number that hit that area over time. Looking back at it, the answer does seem to be in the ballpark. It was a multiple choice answer in which all of the answers were wrong. However, all of them are in the 1015 range, which agrees with my answer.

Last edited:
OmegaFury said:
Oh. I think I see what you're getting at. Electric current already incorporates the cross-sectional area as part of the equation. When calculating for the number of protons, you do calculate for the total number that hit that area over time. Looking back at it, the answer does seem to be in the ballpark. It was a multiple choice answer in which all of the answers were wrong. However, all of them are in the 1015 range.

I don't see how to get an answer much different from what you got in post 3. Unless they forgot to include part of the problem or something.

I'm pretty certain that was the way to go about solving it. Thanks for the help. I appreciate it.

## 1. How does a particle accelerator work?

A particle accelerator uses electromagnetic fields to accelerate particles to high speeds and then collide them with a target. In the case of a proton beam colliding with a target, the particles are accelerated using electric fields and guided by magnetic fields.

## 2. What is the purpose of using a proton beam in a particle accelerator?

Proton beams are used in particle accelerators because they have a high mass and charge, making them ideal for studying the fundamental building blocks of matter. The collisions between the proton beam and the target can create new particles and provide insights into the nature of the universe.

## 3. How is the target material chosen in a particle accelerator?

The target material is chosen based on the specific research goals of the experiment. It needs to be able to withstand the high energies of the proton beam and also produce the desired particles when struck. Common target materials include metals, gases, and liquids.

## 4. What safety precautions are taken when operating a particle accelerator?

Particle accelerators are complex and powerful machines, so strict safety protocols are in place to protect both the scientists and the public. These include shielding to contain any radiation produced during collisions, emergency shutdown procedures, and thorough training for anyone working with the accelerator.

## 5. What are some potential applications of the research conducted with particle accelerators?

The research conducted with particle accelerators has many potential applications. It can help us understand the fundamental laws of physics, develop new technologies, and advance medical treatments such as cancer therapy and imaging. Particle accelerators are also used in industrial processes such as sterilizing medical equipment and detecting impurities in materials.

• Introductory Physics Homework Help
Replies
3
Views
3K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
20
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
792
• Introductory Physics Homework Help
Replies
3
Views
3K