# Basic high school algebra, with physics

1. Feb 11, 2010

### forrealfyziks

"basic high school" algebra, with physics

1. The problem statement, all variables and given/known data
Consider a head-on, elastic collision between a massless photon (momentum po and energy Eo) and a stationary free electron. (a) Assuming that the photon bounces directly back with momentum p (in the direction of -po) and energy E, use conservation of energy and momentum to find p.

2. Relevant equations
E=$$\gamma$$mc2
p=$$\gamma$$mu
massless: E=pc
rest mass: E=mc2
E2=(pc)2+(mc2)2
v/c=pc/E
$$\gamma$$=1/$$\sqrt{1+(v/c)^2}$$

3. The attempt at a solution
Note:First of all I know that this is relativity, but it boils down to just plain algebra. I can't figure it out and help is hard to find, so if you can help I would really appreciate it.

I assume that p is the momentum of the electron. m=mass of the electron u=velocity of the electron c=speed of light

conserving energy: poc+mc2=pc+$$\gamma$$mc2
po+mc=p+$$\gamma$$mc
po=p+$$\gamma$$mc-mc

conserving momentum: po=p-p=$$\gamma$$mu-p

Plugging the result I got in conserving energy into the momentum equation:
p-p=p+$$\gamma$$mc-mc
p=2p+mc($$\gamma$$-1)

2. Feb 12, 2010

### kuruman

Re: "basic high school" algebra, with physics

The problem with the last line is that gamma has the speed of the electron (an unknown quantity) buried in it. Forget gamma. Write the energy conservation equation as

$$p_{0}c+mc^2=pc+\sqrt{(p_ec)^2+m^2c^4}$$

where pe is the final momentum of the electron.

Use the momentum conservation equation to replace pe with what it is equal to, then solve for p.