Basic high school algebra, with physics

[forrealfyziks]

"basic high school" algebra, with physics

Homework Statement

Consider a head-on, elastic collision between a massless photon (momentum p_o and energy E_o) and a stationary free electron. (a) Assuming that the photon bounces directly back with momentum p (in the direction of -p_o) and energy E, use conservation of energy and momentum to find p.

Homework 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/$$\sqrt{1+(v/c)^2}$$

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: p_oc+mc²=pc+$$\gamma$$mc²
p_o+mc=p+$$\gamma$$mc
p_o=p+$$\gamma$$mc-mc

conserving momentum: p_o=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)

 

[kuruman]

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 p_e is the final momentum of the electron.

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