Equation used to find kinetic energy of proton

[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!

 

[stedwards]

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...

 

[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?

 

[jtbell]

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.

 

[jtbell]

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!

 

[jtbell]

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?