Quantum: Photon strikes Electron.

[Yashir1992]

A 120nm photon strikes an electron in a head on collison causing the elctron to be moved in the forward direction and the photon to rebound directly back.
A. Calculate the inital speed of the Electron after colison.
B. Calculate the wavelength of the rebounding Photon.



E=H/f
E = W+Ek
p= H/Wavelength

Givens: C= 3.0x10^8m/s
H = 6.63x10^-34J*S


Although the problem being linear simplifies it a bit, i still had trouble with it. so here i go.

Equation one.
E(prime)= HC/Wavelength - 1/2mv^2
HC/Wavelength(prime) = HC/Wavelength - 1/2mv^2

Equation two.
HC/Wavelength(prime) = -HC/Wavelength + Cmv

Therefore
HC/Wavelength - 1/2mv^2 = -HC/Wavelength + Cmv

Rearranged this makes: (some parts already calculated for simplicity sake)
3.32x10^-8J / (c)(m^2)(2) = v+v^2
3.32x10^-8J / 4.98x10^-52 = v+v^2
6.67x10^59 = v+v^2
Squareroot(6.67x10^59/2) = v
5.77x10^29 = v
But this answer must be wrong since its going way faster then the speed of light.
maybe some clarification on where i went wrong or if i made some silly math error would be awesome.

 

[vela]

Your first two equations look good, but something went awry after you rearranged. The right side isn't correct because the units don't work out. You can't add v to v^2. There's probably a factor of c missing. Not surprisingly, the units on the left side look messed up too.

Your setup looks good, but I think you made an algebra mistake somewhere.

 

[Yashir1992]

Yeah, iv just figured out that you had to use a Quadratic formula instead of rearanging. i found my mistake and corrected it and answered the question the right way, but thanks for taking a look at it.