# Homework Help: Decay into photons

1. Nov 29, 2009

### mathman44

1. The problem statement, all variables and given/known data

A mass M moving at speed V going east decays into 2 photons. One moves perpendicular (south) and the other at some angle from the horizontal. Show that if tan(theta) = 1/2, then V/C = [sqrt(5)-1] / 2

3. The attempt at a solution

(gamma is the lorentz factor)

Momentum in x: x momentum of angled photon: gamma*m*v
Momentum in y: y momentum of angled photon = momentum of perpendicular photon = E1/C

Solving for E1, I get mc^2/2*gamma

Since tan(theta) = 1/2 = [P in y]/[P in x]

then 1/2 = [E1/C]/[gamma*m*v]

I get V = C/gamma^2...

2. Nov 29, 2009

### tiny-tim

Hi mathman44!

Why gamma?

Photons travel at the speed of light.

3. Nov 29, 2009

### mathman44

Conservation of momentum says that the x momentum of the angled photon is equal to the x momentum of the mass before decay... right? So to find the momentum of the mass before decay, I need gamma.

4. Nov 29, 2009

### Redbelly98

Staff Emeritus
Looks good so far. What is gamma, by definition?

5. Nov 29, 2009

### mathman44

gamma = 1/sqrt(1 - v^2/c^2)

:S?

6. Nov 29, 2009

### tiny-tim

oh i see, you're using gamma for the mass M …

but you need the momentum of both photons, and you also need conservation of energy.

7. Nov 29, 2009

### mathman44

I used cons momentum with both photons, no?

y: momentum of photon 1 = momentum of photon 2
x: momentum of photon 2 = momentum of mass before decay

where photon 2 is the angled one. I have already solved for E1, so what do I need cons. of energy for?

8. Nov 29, 2009

### Redbelly98

Staff Emeritus
You can combine these equations to find v

9. Nov 29, 2009

### mathman44

Then V = C - V^2/C? Doesn't make sense to me...

10. Nov 29, 2009

### tiny-tim

actually, V2/c = 1 - V2/c, but still gives the wrong answer
mathman44, i don't know how you solved for E1, but you do need cons. of energy

11. Nov 29, 2009

### mathman44

Yes, you're right... my teacher gave us E1 in class. Does

gamma*m*c^2 = p1c + p2c

look good? And if so, I don't know p2 so how can I solve for p1c (E1)? My brain hurts.

12. Nov 29, 2009

### tiny-tim

Yes, but split p2 into x and y components, and use Pythagoras.

(going to bed now … goodnight! :zzz:)

13. Nov 29, 2009

### Redbelly98

Staff Emeritus
If you solve this quadratic equation in v, you'll get the answer you are supposed to get.

There is a problem with inconsistent units here

Hmmm, I'm also puzzled how E1 was solved for. But mathman44's equation does yield the same answer given in the problem statement.

14. Nov 29, 2009

### Redbelly98

Staff Emeritus
In that case, you don't need conservation of energy. Presumably it was already used by your teacher to determine E1.