Matter/antimatter annihilation question

[chris_183]

Although this question is simple it's been bugging me:

If you were to take one kilo of antimatter and annihilate it with one kilo of matter is the energy (using E=mc^2) released proportional simply to the mass of the matter or to the sum of the masses of both the matter and antimatter?

So is the energy released :

E=mc^2=1*299792458^2= 89875517873681760 Joules

or E=mc^2=2*299792458^2= 179751035747363520 Joules

?

Cheers in advance :tongue:

 

[Astronuc]

If one has 1 kg of matter and 1 kg of anti-matter, then energy related to mass is 2 kg. However, the energy is not completely released as kinetic energy or EM energy directly.

While positron + electron annihilate to produce two gamma rays, proton + antiproton produce pions (or rarely Kaons), which decay to muons (if pions are charged) or gammas or e⁺-e^- pairs (if pions are neutral), and muons decay to electrons and neutrino/anti-neutrinos. So there is some mass retained, but very briefly.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/piondec.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/lepton.html#c3

Review the half-lives of pions and muons.

Given the tremendous energy from the first annihilations, it would be difficult to contain the masses of matter and anti-matter to ensure complete annihilation.

 

[sir-pinski]

This is a great question! The answer is actually the second option - the energy released is proportional to the sum of the masses of both the matter and antimatter. This is because when matter and antimatter annihilate, they release energy in the form of photons (light) that have an energy equivalent to the sum of the masses of both particles. So in your example, the energy released would be 179751035747363520 Joules.

This concept is known as mass-energy equivalence, which is described by the famous equation E=mc^2. This equation shows that mass and energy are interchangeable and can be converted into each other. In the case of matter and antimatter annihilation, the mass is completely converted into energy, resulting in a very large release of energy.

I hope this helps to clear up any confusion you had about this topic. Keep asking great questions and exploring the fascinating world of physics!