What is the relationship between mass and energy according to E=MC^2?

[jaydnul]

Quick question... does that equation refer to any type of matter, like a point particle? Or does it refer to atoms that have nuclei that are attached by the strong force? Lemme put it another way. Take a point particle, an electron... now if you found a way to convert that single electron into energy, would e=mc^2 calculate how much energy that would be? Or does e=mc^2 just refer to the energy inside an atomic nucleus aka the strong force?

 

[Bandersnatch]

That equation concerns energy of any mass at rest.
If it has got rest mass and is not moving, then it's got that energy.
You can use it to calculate the energy released from the annihilation of an electron with a positron.

Also, I'm pretty sure the "point particle" status of an electron is just an approximation, not actual physical reality.

 

[jaydnul]

So when u-235 is split the energy released isn't equal to (mass of uranium)*(c^2) right? Because a majority of that mass is still there just in two different pieces.

 

[Nugatory]

So when u-235 is split the energy released isn't equal to (mass of uranium)*(c^2) right? Because a majority of that mass is still there just in two different pieces.

Yes. Uranium fission only releases a very small fraction of the total mass-energy of the uranium atom. The U-235 bomb that destroyed Hiroshima in 1945 contained about 50 kilograms of U-235, of which a bit less than one kilogram fissioned before the bomb blew apart. The explosion released maybe 5x10¹³ Joules of energy, meaning that about .5 grams of mass was converted to energy.

(These are round numbers because I'm doing the calculations in my head. Google will find you more precise numbers, but I've got the ranges of sizes about right).

 

[jaydnul]

ahh very interesting. thanks!

Also something that has me a little confused is this: since nuclear fission releases energy, it seems that nuclear fusion should consume energy given that its the opposite of fission. But that's not the case because the sun runs on nuclear fusion. Why is that?

 

[jtbell]

For light isotopes, fusion tends to release energy and fission tends to require energy input. For heavy isotopes, it's the other way around. The "turnover point" is around iron. Google for "binding energy curve" and you'll probably turn up explanations.