# How much energy is released from an electron-positron annihilation?

1. Dec 17, 2011

### thomas9459

More specifically, I am wondering what the energy released is when the electromagnetic force is also included in this calculation. In the case where the electron and positron are at a distance d, the energy released would be the mass energy (1.022 MeV) plus the energy that resulted from the electromagnetic attraction. Using Coulomb's Law, the energy released should be infinite, which is obviously not the case. What does QED say about the mater? Has an experiment which measured the energy released accurately enough to see the extra energy from the electromagnetic attraction?

2. Dec 17, 2011

### mathman

3. Dec 17, 2011

### thomas9459

That still doesn't answer the question of how much energy is released from the annihilation.

4. Dec 18, 2011

### CyberShot

I'm a layman but I'd think that since the both particles are being annihilated, that no energy is released; don't they just cancel each other out?

5. Dec 18, 2011

### Fightfish

That violates conservation of energy and is certainly not true at all.

Pal, you don't have to drag in QED in order to describe this phenomenon! This is perfectly describable using basic physics - the concept of conservation of energy (or rather, mass-energy in this case).

Imagine I have a system consisting of an electron and positron at a distance d from each other. The total energy of the system at that point is
$$m_{e}c^{2} + m_{p}c^{2} + KE_{e} + KE_{p} - k \frac{e^{2}}{d^{2}}$$
By conservation of mass-energy, the total energy released when they annihilate is the same.

6. Dec 18, 2011

### thomas9459

So a better question is at what distance do they annihilate. My impression was it happens when the electron and positron "touch", but since they are point particles, this would happen at d=0, which results in a division by zero.

7. Dec 18, 2011

### Morgoth

you try to mix quantum mechanics with classical mechanics in not a good way and thus you result in this problem.
The phenomenon of annihilation is an electromagnetic one, thus you truly have electromagnetism already inside.
Generally it doesn't happen when they "touch". It happens in whatever a distance they are according to the possibilities of electromagnetism interaction (thus the coupling constant). Thus you have annihilation as you also have the pair creation of a photon of E_g ~> 1MeV (eg Na22)