Photon colliding with stationary mass

[Dennydont]

Homework Statement

A photon with energy E collides with stationary mass m. They form a single particle together, what is this new particle's mass and what is its speed?

Homework Equations

Energy-momentum 4-vector P=(E, p_x, p_y, p_z)
Possibly P²=m²

The Attempt at a Solution

Using 4- momenta, the particle moving with energy E has a 4-momenta of P₁ = (E, p, 0, 0) and the stationary mass is P₂ = (m, 0, 0, 0). The total momentum before the collision is then P_before = (E+m, p, 0, 0). My question is, what exactly would the P_after equal to? Could it possibly be: P_after = (E', p', 0, 0)
If so that would show that E' = E+m (due to conservation of energy). How can I find the mass of the new particle from that? Does the second equation of m² have anything to do with it?[/SUB]

 

[Orodruin]

How can I find the mass of the new particle from that?

You have the expression for the mass of a particle right here:

Possibly P2=m2

 

[Dennydont]

You have the expression for the mass of a particle right here:

Great, do I have all the tools to solve this then? Is P_after = (E', p', 0, 0) correct? How can I find the speed then?

 

[PeroK]

Great, do I have all the tools to solve this then? Is P_after = (E', p', 0, 0) correct? How can I find the speed then?

For a particle you have three important equations that you must not forget:

$E = \gamma mc^2$

$p = \gamma mv$

$E^2 = p^2 c^2 + m^2 c^4$

In particular, if you know the energy and momentum of a particle, you can calculate its mass, velocity and gamma factor.

You should experiment with these equations to see how you can do this.

 

[Dennydont]

For a particle you have three important equations that you must not forget:

$E = \gamma mc^2$

$p = \gamma mv$

$E^2 = p^2 c^2 + m^2 c^4$

In particular, if you know the energy and momentum of a particle, you can calculate its mass, velocity and gamma factor.

You should experiment with these equations to see how you can do this.

These equations are rather useful, but I just want to know if Pafter = (E', p', 0, 0). If so I can substitute E' as E+m and p' as p, using conservation of energy and momentum laws. Thanks to the third equation you've given me, I can say that p = √(E²-m²) and p' = √(E²-m²) and solve for m' since we are saying that c=1 in this example. I can't see why Pafter isn't what I think it is, the new particle doesn't travel on an angle or anything like that.

 

[Orodruin]

Great, do I have all the tools to solve this then? Is P_after = (E', p', 0, 0) correct? How can I find the speed then?

The 4-momentum is proportional to the 4-velocity. You can use this fact to find the speed. In other words, how would you find the speed if I gave you a 4-velocity?

 

[PeroK]

These equations are rather useful, but I just want to know if Pafter = (E', p', 0, 0). If so I can substitute E' as E+m and p' as p, using conservation of energy and momentum laws. Thanks to the third equation you've given me, I can say that p = √(E²-m²) and p' = √(E²-m²) and solve for m' since we are saying that c=1 in this example. I can't see why Pafter isn't what I think it is, the new particle doesn't travel on an angle or anything like that.

You should satisfy yourself from conservation of momentum that the final particle must move in the same direction as the photon.

Also, I think you're missing the relationship between the energy and momentum of a photon. Hint: only one of those three equations holds for a photon.

 

[Orodruin]

You should satisfy yourself from conservation of momentum that the final particle must move in the same direction as the photon.

Also, I think you're missing the relationship between the energy and momentum of a photon. Hint: only one of those three equations holds for a photon.

I do not think the problem is what you perceive it is. A student using 4-vector notation should already be familiar with what you have said, which is essentially the statement of the components if the 4-momentum for a massive particle.