# Relativistic momentum and energy of a particle

1. Sep 5, 2009

### w3390

1. The problem statement, all variables and given/known data

In a certain reference frame, a particle with momentum of 7 MeV/c and a total energy of 9 MeV. Determine the mass of the particle. I did not mistype this problem, this is the way it appears on my assignment.

2. Relevant equations

Total Relativistic Energy: E^2=p^2c^2+(mc^2)^2

3. The attempt at a solution

I figured that since I am given the total energy of the particle and the momentum of the particle, I could plug those values in and solve for m. However, this gives me the wrong answer. I also tried taking both values given and converting them to joules so that my answer for mass would be in kilograms and then converting to eV, but that didn't work either. Any suggestions?

2. Sep 5, 2009

### kuruman

The total energy equation is correct and so is you approach. So unless you show what did in some detail we cannot help you. Also, how do you know the answer is wrong?

3. Sep 5, 2009

### w3390

Okay, here's my work:

E$$^{2}$$=p$$^{2}$$c$$^{2}$$+(mc$$^{2}$$)$$^{2}$$

(1.44E-9)$$^{2}$$=(1.12E-9)$$^{2}$$(3E8)$$^{2}$$+m$$^{2}$$(3E8)$$^{4}$$

(2.0736E-18)=(1.2544E-9)(9E16)+m$$^{2}$$(8.1E33)

m=1.18E-13 kg

Then using this conversion: (1000 Mev/c$$^{2}$$=1.783E-27kg)
I found that 1.18E-13 kg = 1.18E-10 $$\frac{MeV}{c^{2}}$$

Oh, do I have to multiply this number by c$$^{2}$$ in order to get my answer in MeV?

4. Sep 5, 2009

### kuruman

You got tangled up with your conversions. You need to get used to the new units. They make sense. Watch the magic:

E2=p2c2+(mc2)2

Plug in the given values without conversion, but keep track of the units

92 (MeV)2=72c2(MeV)2/c2+(mc2)2

92 (MeV)2-72(MeV)2=(mc2)2

Solve this for the rest mass (mc2) in MeV and convert to kg if you wish.

5. Sep 5, 2009

### w3390

Thanks a lot kuruman, I didn't even think to solve for the rest mass.