Electron Velocity: Answering 2 Questions in a Vacuum

[HarryDaniels]

Two questions
Both of these occur in a vacuum:
If a photon has the exact energy to electron-positron pair product, since the electron and the positron are the same mass, if stationary would have an energy of Mc^2. Since they are moving would there energy be (of one fermion):

E=(mc^2)+(1/2mv^2)
or
E=mc

If that is true does that mean the energy of the photon (in a vacuum) would be:

Ey=2((mc^2)+(1/2mv^2)
or
Ey=2(mc^2)

Then, in a vacuum, would the electron and the positron collide? The second question is the previous one and what is velocity needed for anihilation?

 

[AndyW]

Hello,

Thank you for your questions. I am happy to provide some answers and clarification on this topic.

Firstly, let's address the energy of the electron and positron in motion. The correct formula is actually E = (mc^2) + (1/2)mv^2. This is known as the total energy, which includes both the rest energy (mc^2) and the kinetic energy ((1/2)mv^2). So, the energy of a moving electron or positron would be given by this formula.

Now, for the energy of the photon in a vacuum. The energy of a photon is given by the formula E = hf, where h is Planck's constant and f is the frequency of the photon. This means that the energy of the photon is directly proportional to its frequency. Therefore, the energy of a photon that can produce an electron-positron pair would be twice the energy of a single electron or positron (since it produces two particles).

In a vacuum, the electron and positron would indeed collide and annihilate each other, releasing energy in the form of gamma rays. The velocity needed for annihilation would depend on the energy of the electron and positron. Generally, the higher the energy, the higher the velocity needed for annihilation to occur.

I hope this helps to answer your questions. If you have any further inquiries, please don't hesitate to ask. As scientists, it is our duty to seek knowledge and share it with others. Keep asking questions and exploring the wonders of the universe.