# Equation used to find kinetic energy of proton

• darksyesider
In summary, the conversation discusses two possible methods for finding the kinetic energy of a proton given its wavelength. The first method is non-relativistic, while the second method takes into account relativistic effects. It is suggested to use the second method as it is more accurate for high-energy particles. The conversation also mentions checking calculations and units carefully, and provides a suggestion for a further check.
darksyesider
I am having trouble deciding when to use which equation.

If you're given the wavelength of a proton, let's say 100 fm, and have to find the kinetic energy of it, how would you do this?

Here are my ideas:

Idea 1: Use lambda = h/p, where p = sqrt(2Em).

Idea 2: Use E=(pc)^2+(mc^2)^2 = (mc^2)^2+(h/lambda * c)^2

Then I'll use:

K = E- E_o
==> (answer from idea 1 or 2) - mc^2 Which should I use? I personally think idea 2 is correct because it accounts for the relativisitic effects.

thank you!

In your idea 1 you've already given the wavelength to momentum relationship---and you're given the wavelength. That's all you need.

Edit: looks like I misread the question...

Last edited:
darksyesider
but is the equation correct?
I actually forgot how I got p = sqrt(2Em)...I think I derived it earlier in my work.

Also I asked my friend who is learning this in school and he said that you have to use idea 2 because it is a particle?

darksyesider said:
Which should I use? I personally think idea 2 is correct because it accounts for the relativisitic effects.

The relativistic equation is correct in general. Your method 1 is basically non-relativistic, so it's "correct enough" only for low-energy (low-velocity) particles. But it's hard to tell in advance whether the velocity is "low enough" unless you have a lot of experience in doing these kinds of problems. So I would go with your method 2. If you have time, try method 1 also and see how close together the results are.

darksyesider
darksyesider said:
I actually forgot how I got p = sqrt(2Em)

Hint: start with the non-relativistic formulas for momentum and kinetic energy, p = mv and E = (1/2)mv2.

darksyesider
Thank you everyone! My answer using method 2 was actually 1000 times larger than the answer using method 1. I guess you have to take into account relativity!

darksyesider said:
My answer using method 2 was actually 1000 times larger than the answer using method 1.

I suggest that you check your calculations and particularly your units carefully. My results for the two methods differ by only about 0.004%.

As a check, calculate the proton's speed assuming the classical formula. What % is it of the speed of light?

## 1. What is the equation used to find the kinetic energy of a proton?

The equation used to find the kinetic energy of a proton is KE = 1/2 * m * v^2, where KE is kinetic energy, m is the mass of the proton, and v is the velocity of the proton.

## 2. How is the mass of a proton determined in this equation?

The mass of a proton is typically given in units of kilograms (kg) and is a constant value that can be found in scientific databases or textbooks.

## 3. What is the unit of measurement for kinetic energy in this equation?

The unit of measurement for kinetic energy in this equation is joules (J). This is the standard unit for energy in the International System of Units (SI).

## 4. How does the velocity of a proton affect its kinetic energy?

The velocity of a proton has a direct relationship with its kinetic energy. This means that as the velocity increases, the kinetic energy also increases. This can be seen in the equation, where v^2 is multiplied by the mass and 1/2, showing that velocity has a significant impact on the kinetic energy calculation.

## 5. Is this equation only applicable to protons, or can it be used for other particles?

This equation can be used for any particle, as long as the mass and velocity are known. However, it is most commonly used for protons due to their prevalence in scientific experiments and calculations.

• Quantum Physics
Replies
5
Views
2K
• Quantum Physics
Replies
15
Views
2K
• Quantum Physics
Replies
6
Views
2K
• Classical Physics
Replies
16
Views
748
• Quantum Physics
Replies
1
Views
919
• Quantum Physics
Replies
5
Views
1K
• Quantum Physics
Replies
9
Views
959
• Quantum Physics
Replies
18
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
54
Views
8K