# Relativistic Momentum of photon

## Homework Statement

How much work is required to accelerate a proton from rest up to a speed of 0.999c?
What would be the momentum of this proton?

p=γmv

## The Attempt at a Solution

I got part A, which was the momentum. I found that to be 20.1 GeV. Now for part B I have to find the momentum in units of GeV/c. I'm down to my last attempt on Mastering Physics. First, I tried going the simplest route and divided the 20.1 GeV from part A by c to get 6.7e-8 and that was wrong. I also tried using p=γmv to find an answer of 1.12e-5 J, which I converted to 7.01e-8 GeV, then divided that by c and got an incorrect figure of 2.34e-16.

Any help would be greatly appreciated.

## Answers and Replies

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PeroK
Science Advisor
Homework Helper
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## Homework Statement

How much work is required to accelerate a proton from rest up to a speed of 0.999c?
What would be the momentum of this proton?

p=γmv

## The Attempt at a Solution

I got part A, which was the momentum. I found that to be 20.1 GeV. Now for part B I have to find the momentum in units of GeV/c. I'm down to my last attempt on Mastering Physics. First, I tried going the simplest route and divided the 20.1 GeV from part A by c to get 6.7e-8 and that was wrong. I also tried using p=γmv to find an answer of 1.12e-5 J, which I converted to 7.01e-8 GeV, then divided that by c and got an incorrect figure of 2.34e-16.

Any help would be greatly appreciated.
Can you find a formula that relates the energy to the momentum of a particle?

Would that be E^2=p^2c^2 + m^2c^4? If that is the correct equation, I came up with an answer of 1.35e-6.

PeroK
Science Advisor
Homework Helper
Gold Member
Would that be E^2=p^2c^2 + m^2c^4? If that is the correct equation, I came up with an answer of 1.35e-6.
You could use that one. But, what about using $E = \gamma mc^2$ and $p = \gamma mv$?

Honestly, I'm not quite sure what I would do with those equations. I saw that a guy on Yahoo Answers did K/c=mvγ and that led me to an answer of 7.01e-8. I'm not confident that that is right though. Any idea if my answer of 1.35e-6 from my previous post is right?

PeroK
Science Advisor
Homework Helper
Gold Member
Honestly, I'm not quite sure what I would do with those equations. I saw that a guy on Yahoo Answers did K/c=mvγ and that led me to an answer of 7.01e-8. I'm not confident that that is right though. Any idea if my answer of 1.35e-6 from my previous post is right?
I think your problem is probably understanding $eV$ units. The mass of a particle is normally given in $MeV/c^2$. For example, the proton mass is about $938 MeV/c^2$.

The energy of a particle is, therefore, $E = \gamma m$ where $E$ is in $MeV$ and $m$ is the mass in $MeV/c^2$.

Momentum is given in units of $MeV/c$ and we have $p = \gamma mv/c$ in these units.

In this case $v/c = 0.999 \approx 1$ so we have $p \approx \gamma m = E$.

These units take a bit of time and practice to get used to, but you can see how using them can simplify the calculations.

Yes, thank you it makes sense now.