Electron - Positron Annihiliation

[qwertyuiop23]

I know that positrons are produced by beta + decay and I know that they are antimatter. My question now comes to what happens when the collide. I know that should be complete annihiliation and the most likely outcome is the production of two or more gamma rays. My question comes when trying to calculate the energy of those rays. Should the energy produced be governed by E = mc^2? If it does and I have done my calculations then the energy released by positron - electron annihiliation 1.6*10^-13 J of energy is released which is not a lot of energy but I would have thought I would see some trace of this energy. And if this theory is then applied to 1 mol of any substance that beta + decay (since the production of positrons is in a 1:1 ratio to the substance decaying) I calculated that we get 9.8*10^10 which is 98 GJ. I have no idea how much that is in relation but it seems a lot.

Could someone verify what I have done here and I haven't made any misconceptions. And if I am correct then where does the 98GJ go when the atom decays.

Cheers
~Qwertyuiop23

 

[CompuChip]

The energy is released in the form of photons, the massless "particles" which make up light. For photons the energy depends on the frequency f through E = h f (where h is another physical constant, just like c). Although the amount of energy per annihilation is very very tiny, a lot of these reactions can provide a lot of energy. This is used in nuclear reactors for example - if you look up some of them on Wikipedia you can see their energy production in the info box, this is of order 10¹⁶ J.

 

[Bob S]

You are correct. Some nucear beta decays emit positrons. Positrons sometimes annihilate with electrons before stopping, but most stop and form an electron-positron "atom" called positronium, and annihilate after a few nanoseconds. The energy released in one annililation is about 1.6 x 10^-13 Joules, and is in the form of two opposing 511-Kev photons. A mole of these annilations would release about 98 GJ of energy. using 120 MJ as the energy in 1 gallon of gasoline, 98 GJ is equivalent to the energy in about 800 gallons of gasoline.