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The person giving the answer below has put a lot of effort in, but the answer is not correct. The (approximate) answer is: 1.637 X 10-13 Joules.
Here's the correct working:
Electron and positron both have mass of about 9.109 X 10-31 kg.
So total mass, m = 2 x 9.109 x 10-31 kg.
The speed of light (in a vacuum) is c = 299,792,458 m/s.
E = mc2. So, put the numbers in the equation, use a calculator and you get the answer: about 1.637 x 10-13 Joules.
I am not a Physicist, I am merely a 9th grader.
However, it seems common sense to use Einstein's equation E=mc2 to solve this.
The energy produced upon an electron being annihilated would be E, and of course, m is the mass of the electron, then multiplied by the speed of light squared. What we'll do is:
E (in Joules)= (Mass of electron in grams) * Speed of light in meters squared
A quick Wikipedia search reveals the mass of the electron is
9.10938291(40) * 10-31 kg
Which I typed into my Scientific Calculator and returned,
3.643753164 * 10-29 kg
I then moved the decimal to the left (10 has a negative exponent) 29 times to get,
0.0000000000000000000000000003643753164 kg.
Now, E=mc2 calculates mass in grams. So we must get rid of three of the zeros:
0.0000000000000000000000003643753164 g
There. We now have the mass of the electron in grams. The positron, as you probably know, has the exact same mass. Now to find the speed of light in meters...
According to Google, the speed of light is: 299 792 458 m/s.
We must square it, and we get:
8.987551787 * 1016
Which translates to,
89875517870000000
So now, we have both the mass of the electron/positron AND the speed of light squared! Lets multiply them!
3.274842026 * 10-08 J (Joules).
There you go.
0.0000003274842026 J.
Not much, isn't it?
But the other day, using the same equation, I (mentally) collided 100g of Hydrogen with 100g of Anti-Hydrogen and got over 17.9 quintillon joules!
I just love physics!
~Lance
The energy produced by an electron-positron annihilation can be calculated using the equation E = mc^2, where E is the energy, m is the mass of the particles (rest mass in this case), and c is the speed of light. The rest mass of an electron is approximately 9.11 x 10^-31 kg, and the rest mass of a positron is the same. Substituting these values into the equation gives the energy produced as 1.64 x 10^-13 joules.
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Annihilation is the process by which a particle and its antiparticle collide and convert their mass to energy, typically resulting in the production of gamma rays. This process obeys the principle of conservation of mass-energy, as the total mass-energy before annihilation is equal to the total mass-energy after annihilation.
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