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Name: Jon P.
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How does nuclear fusion result in excess energy?


This is best explained by Einstein's most famous equation, E = mc^2. You are probably familiar with this, but let me go over it just in case you are not. "E" represents energy, "m" is mass and "c" is the speed of light. This equation shows the correlation between mass and energy, with a simple constant. However, the constant is a very large number and it gets even larger because it is squared. This means that even very tiny amounts of mass can result in the release of enormous amounts of energy.

This equation relates to fusion very intimately. Fusion is the process by which two deuterium atoms, (or one hydrogen and one tritium atom) combine to form Helium. If you add up the mass of two deuterium atoms, you will notice that Helium is very slightly lighter. Since the nucleus of a Helium atom is very stable (due to its full valance shell), it results in a lower energy needed to hold the nucleus together. I do not know the exact mechanism of fusion, so I cannot get much more detailed than this. Helium is much more stable than deuterium, so the amount of energy of energy given off is pretty large. This results in a minor loss of mass and can be seen by observing the actual masses of deuterium (2.013553 u) versus Helium (4.002602 u). The mass difference is 0.0245 u, where u is grams per mole of atoms. Avogadro's number (number of atom in a mole) is 6.022 x 10^23, which means that the actual mass change in one atom is so very small--just 0.61% decrease in mass. But remember that the speed of light squared is equal to 89875517873681764 meters per second. So for one mole of gas the result is an enormous amount of energy (0.0245 x c^2).

Note that I have not done unit analysis, so if you want to solve some problems, make sure that you are using mass, energy and c with proper units.

Matt Voss

Dear Jon P. I do not know what you mean by excess energy. However, I do know that energy is conserved if you count all kinds of energy.

Since a helium nucleus is very strongly bound by the strong force, its mass is considerably less that the mass of two (comparatively lightly bound) deuterium nuclei. And since, as Einstein taught us (E = mc^2), mass is a form of energy, some of the mass energy of the deuterons must be transformed into other forms of energy (like heat).

The same thing happens when you burn coal where C and O2 combine to CO2 with a reduction in mass. However, fusion produces about a million times greater percentage reduction in mass, which explains the fearsome power of nuclear weapons and the relatively tiny amount of uranium needed to fuel nuclear reactors.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University

Jon P.,

Energy from fusion and energy from fission are based on Einstein's famous relationship between mass and energy: E=mc^2. Both fission and fusion can transform mass into energy. A standard fusion reaction is joining four hydrogen atoms into one helium atom. Two hydrogen atoms (one proton and one electron) join into a heavy hydrogen atom (one proton and neutron with one electron). The extra electron joins with its proton to produce the neutron. This heavy hydrogen atom is called deuterium. Two deuterium atoms then join into one helium atom. The four hydrogen atoms we started with have greater mass than the one helium atom we end with. The lost mass is released as radioactive energy. Although very little mass is lost, multiplying the small mass by the square of the speed of light results in a large amount of energy.

Fusion requires high temperature because hydrogen atoms must be extremely close together before they will fuse together. A hydrogen molecule's two atoms are not close enough together to fuse. If the hydrogen is extremely hot, the atoms are moving fast enough to have the nucleus of one crash into the nucleus of another. This can result in fusion. A standard hydrogen bomb requires an atomic bomb as a trigger. An ordinary chemical bomb would not provide a high enough temperature.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College

When two nuclei fuse, the sum of the masses of those nuclei is less than the sum of the initial nuclei. That energy difference is converted into energy according to Einstein's famous formula delta E = delta M x (c^2). Because of the size of the quantity (c^2), a small mass loss creates a large amount of energy that is given off by a variety of fusion processes.

Vince Calder

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