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

#### max8404

1. 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.

2. Homework Equations

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

3. 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!

Related Introductory Physics Homework Help News on Phys.org

#### 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

2. 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

Re: congratulations!

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

Homework Helper
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

Staff Emeritus
Homework Helper
I have a big problem with a photon's velocity being less than c.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving