# Rest energy and Kinetic Energy of a Photon - velocity?

## Homework Statement

Thanks for everyone that helped me with the physics questions! I had my physics 2 final today and got a 94!!! There was a question that I could not figure out for a long time. It goes like this.

What would the velocity of the photon be if the Kinetic energy of the photon equals the rest energy of the photon? Express v in terms of c and anything else. Luckily, the question was a multiple choice, and the correct answer (which I guessed) was sqrt(3)/2 x c

I still cannot figure out why this is true.

## Homework Equations

K=1/2mv^2 --> I assume this is the right equation to use...
Er=mc^2

## The Attempt at a Solution

Equaling the two would give you:

1/2mv^2=mc^2

v^2=2c^2
v=sqrt(2) x c

This is obviously not true since you can't go faster than the speed of light. Can someone explain to me how the answer is sqrt(3)/2 x c and why I am getting this thing wrong? Am I using the right Kinetic Energy equation??

Thanks!

tiny-tim
Homework Helper
congratulations!

Hi max8404! Many congratulations!! What would the velocity of the photon be if the Kinetic energy of the photon equals the rest energy of the photon? Express v in terms of c and anything else. Luckily, the question was a multiple choice, and the correct answer (which I guessed) was sqrt(3)/2 x c

## Homework Equations

K=1/2mv^2 --> I assume this is the right equation to use...
… why I am getting this thing wrong? Am I using the right Kinetic Energy equation??

oooh, I wish examiners wouldn't use "kinetic energy" in relativity they just mean total energy minus rest energy so 2m = m/√(1 - v2/c2), so 1 - v2/c2 = 1/4 Hi max8404! Many congratulations!! oooh, I wish examiners wouldn't use "kinetic energy" in relativity they just mean total energy minus rest energy so 2m = m/√(1 - v2/c2), so 1 - v2/c2 = 1/4 Hey Tiny Tim, thanks for your response, but I doon't quite get it. I understand the equation,
E=KE+mc^2, but in this case, what would E be? Or am I once again looking at it the wrong way?

Thanks!

tiny-tim
E is the total energy (or relativistic energy), mc2/√(1 - v2/c2) E is the total energy (or relativistic energy), mc2/√(1 - v2/c2) 