Rest energy and Kinetic Energy of a Photon - velocity?

[max8404]

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]

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

 

[max8404]

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)

 

[max8404]

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

duh. thanks a lot! I got it now! :)

 

[Redbelly98]

I have a big problem with a photon's velocity being less than c.