Another energy and momentum SR problem

1. Aug 3, 2008

zimo

1. The problem statement, all variables and given/known data
A 100kev photon scatters from a free electron initially at res. Find the recoil velocity of the electron if the photon scattering angle is 180 degrees.

2. Relevant equations
Conservation of Energy, Conservation of Momentum
(It is not allowed to use Compton's effect equation!)

3. The attempt at a solution
I've written:
\eqalign{ & {{hc} \over \lambda } + m_e c^2 = {{hc} \over {\lambda '}} + {{m_e c^2 } \over {\sqrt {1 - {{\bar v^2 } \over {c^2 }}} }} \cr
$$& {h \over \lambda } = {{m_e \bar v} \over {\sqrt {1 - {{\bar v^2 } \over {c^2 }}} }} - {h \over {\lambda '}} \cr}$$

but as I develop the equations on trying to solve the equations, somewhat it doesn't work out...

2. Aug 3, 2008

tiny-tim

Hi zimo!

Well, you want v, but you don't want $$\lambda'$$ …

so just multiply the second equation by c, and add it to the first equation.

3. Aug 3, 2008

zimo

OK.

Did I write the equations correctly?

4. Aug 3, 2008

tiny-tim

Looks ok to me.

5. Aug 3, 2008

zimo

because I get v=0.483c, in contrast to the final answer in the book, which is 0.319c.

6. Aug 3, 2008

tiny-tim

Unless you show your full calculations, we can't see where you've gone wrong.

7. Aug 3, 2008

zimo

I attached my solution. (starting with the lines indicating I) and II) )

File size:
14.5 KB
Views:
49
8. Aug 4, 2008

9. Aug 4, 2008

Hootenanny

Staff Emeritus
Your attachment needs to be approved by a moderator before we can view it. Be patient, attachments are usually approved fairly quickly. If it hasn't been approved by this evening I'll see if I can get someone's attention.

10. Aug 5, 2008

tiny-tim

Hi zimo!
That's with (.711/.511)2 = 1.936.

The book seems to have used .711/.511 = 1.391, giving the answer of .319

The book seems to be wrong.

11. Aug 5, 2008

zimo

No.

I made an error during the strike-out of (u+1) on both sides, I needed to leave one (u+1) at the right side of the eqation.

Finally, I got 0.319 as requested.