Sum of the energies of the two photons

[badwallpaper0]

Homework Statement

A positron has the same mass as an electron but is of opposite sign (9e-31 kg).
What is the sum of the energies of the two photons which are produced when the positron and the electron annihilate?
Assume the speed of the positron is .93c (c is the speed of light) with an electron at the same speed.

Homework Equations

I truly don't know of any equations except e- + e+ => [tex]\gamma[/tex] + [tex]\gamma[/tex]

[tex]c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}[/tex]

The Attempt at a Solution

I squared the velocity .93c^2 and multiplied it by the mass (9e-31 kg) to find Joules (since the answer must be in Joules).
I'm don't know what else one could do.

Even a hint as to which equations to use would be great.

 

[Reshma]

Use the law of energy conservation. The minimum energy an electron can have is its rest energy i. e. [itex]m_ec^2[/itex]. The total energy is the sum of the rest energy and the Kinetic energy. [itex]E = m_ec^2 + K[/itex]. You have been given the speed of the electron and the positron. Can you calculate their total energy?

 

[Moetasim]

The equation you have provided, e- + e+ => \gamma + \gamma, is actually the equation for electron-positron annihilation, which is the process that produces the two photons in this scenario. In this process, the total energy of the system (consisting of the positron and electron) is converted into the energy of the two photons.

To find the total energy of the system, you can use the equation E = mc^2, where E is the total energy, m is the mass, and c is the speed of light. Since the positron and electron have the same mass, the total energy of the system would be twice the energy of either particle (since there are two particles in the system).

So, to find the sum of the energies of the two photons, you would need to find the total energy of the system and then divide it by 2. To do this, you can use the equation E = mc^2 and plug in the mass and velocity of the particles. Remember to convert the mass of the particles from kg to kg/c^2 before plugging it into the equation.

Once you have the total energy of the system, you can divide it by 2 to find the energy of each photon. Keep in mind that the energy of each photon will be the same, since the photons are produced in pairs in this process.

I hope this helps!