Finding some quantities of particles moving relativistically

[ForTheGreater]

Homework Statement

A 2.5 MeV photon is moving in positive x-direction and an electron in the opposite direction at a velocity of 0.99c. Calculate their common total energy, momentum and total rest mass.

Homework Equations

Relativistic Equations

The Attempt at a Solution

I have some concerns with the statement of the question. First of all how is it relevant that the particles are going in opposite direction?

Not sure how to go about calculating the momentum of a photon since it has no mass, and would it ever get a relativistic rest mass?

When asked about the rest mass of the electron, how is that not just the table value? It's the relativistic mass that would need calculating.So I would like some help with this early exercise to get me going in the right way to think about such a problem. All examples in the textbook has been about observing a moving inertial frame of reference and finding the relativistic variables. This is quite different. Especially since a photon always moves at the speed of light.

 

[mfb]

First of all how is it relevant that the particles are going in opposite direction?

It will influence all three values you are supposed to calculate.

Not sure how to go about calculating the momentum of a photon since it has no mass

There is a simple formula relating the energy to the momentum.

and would it ever get a relativistic rest mass?

No.

When asked about the rest mass of the electron, how is that not just the table value?

The problem asks about the total rest mass, which is the invariant mass of the electron+photon system.

Forget the concept of relativistic masses, it is not used any more in science.

 

[Orodruin]

Photons carry momentum p = E/c. In relativity, mass is not required for an object to carry momentum. The fundamental relationship between energy, momentum, and mass is $E^2 = p^2 + m^2$.

You are being asked for the total combined energy and momentum and invariant mass of the system containing the photon and electron, this is not the same as asking for their individual properties.

 

[ForTheGreater]

It will influence all three values you are supposed to calculate.

How?

 

[mfb]

Calculate it and you'll see.

Here is an intuitive analogy: bumping into a car at a highway that moves in the same direction as you is different from a collision with a car moving at the same speed in the opposite direction.