# What the ?

1. Oct 10, 2004

### Phymath

what the !?

ok idk if im right and the book is wrong but help me out the question is...

An electron moving at a speed 0.60c collides head on witha positron also moving at 0.60c. Determine the energy and momentum of each photon produced in the process.

well this is what I did..
$$E = 2\frac{m_ec^2}{ \sqrt{1-\frac{(0.6c)^2}{c^2}}}$$
$$E = 255864.36 \ eV = 0.256 \ MeV$$
the book says the energy is E = 0.64 MeV why?

i figured E = m_e c^2 + KE but it my calcs must be off or something i don't understand

Last edited: Oct 10, 2004
2. Oct 10, 2004

### Integral

Staff Emeritus
you are not using the correct velocity. Since both electrons are moving at .6c you must compute the speed of the collision using the relativistic formula for addition of velocities.

3. Oct 10, 2004

### Fredrik

Staff Emeritus
Integral: That was my first thought too, but no one said we're supposed to do the calculation in the electron's rest frame. He is doing the calculation in the center-of-mass frame, which is OK.

Phymath: That square root is 0.8, so the quantity you call E (the sum of the two energies), is just 2.5 times the rest mass of the electron, which is 0.511 MeV. So it looks like you just did a very simple calculation error. 2.5 times 0.511 is not 0.25.

4. Oct 10, 2004

### Hurkyl

Staff Emeritus
5. Oct 10, 2004

### Fredrik

Staff Emeritus
Wow, that was cool! I had no idea you could do that.

6. Oct 10, 2004

### Phymath

i understand the .8 error but still it does not give the correct energy value...

7. Oct 11, 2004

### Fredrik

Staff Emeritus
Divide it by 2. There are 2 photons. (They must have the same energy because the total momentum is 0 in this frame).