LOCOM/E and Nuclear Weapons

[Built To Last]

Can someone explain to me the connection between the Law of Conservation of Mass/Energy and Nuclear Weapons.

[Ford Prefect]

http://tomclegg.net/conservation

Good question, but I'm gonna move this to Math and Science.

[rabbit boy]

http://en.wikipedia.org/wiki/Binding_energy
"Binding energy is the mechanical energy required to disassemble a whole into separate parts. The usual convention is that this corresponds to a positive binding energy."

Here's something for you. I'm kind of afraid to screw up explaining it, since I don't know a whole lot about it. I'll try, though.

Basically, all energy has mass, and that contributes to the mass of atomic nuclei and atoms. When you make an atomic nuclei bigger by adding a neutron or proton, for lighter elements this increases the binding energy and decreases the potential energy. Energy is released, and mass decreases. That's fusion for you. Mass defect actually occurs any time there are binding forces involved, but the binding forces of the nuclei of an atom are so large that there's a detectable change of mass.

Binding energy generally increases as you get larger nuclei until you hit iron and nickel. But once you go above them, binding energy per nucleon decreases. Apparently these changes are caused by the balance between the electromagnetic force and the strong nuclear force in the nucleus. Anyway, if you can increase the binding energy of an atomic nucleus you release energy and convert mass to energy (so to speak). Fusion of lighter elements to create heavier nuclei does this, and fission of heavier, unstable nuclei also does this.

Oh, and the equation to convert from mass to energy and vice versa is of course E = mc^2

Other information I got came from the nuclear fusion article:
http://en.wikipedia.org/wiki/Nuclear_fusion#Requirements

[RoundElephant]

E=mc^2 sums it up.

[Mathematics]

http://en.wikipedia.org/wiki/Binding_energy
"Binding energy is the mechanical energy required to disassemble a whole into separate parts. The usual convention is that this corresponds to a positive binding energy."

Here's something for you. I'm kind of afraid to screw up explaining it, since I don't know a whole lot about it. I'll try, though.

Basically, all energy has mass, and that contributes to the mass of atomic nuclei and atoms. When you make an atomic nuclei bigger by adding a neutron or proton, for lighter elements this increases the binding energy and decreases the potential energy. Energy is released, and mass decreases. That's fusion for you. Mass defect actually occurs any time there are binding forces involved, but the binding forces of the nuclei of an atom are so large that there's a detectable change of mass.

Binding energy generally increases as you get larger nuclei until you hit iron and nickel. But once you go above them, binding energy decreases. Apparently these changes are caused by the balance between the electromagnetic force and the strong nuclear force in the nucleus. Anyway, if you can increase the binding energy of an atomic nucleus you release energy and convert mass to energy (so to speak). Fusion of lighter elements to create heavier nuclei does this, and fission of heavier, unstable nuclei also does this.

Oh, and the equation to convert from mass to energy and vice versa is of course E = mc^2

Other information I got came from the nuclear fusion article:
http://en.wikipedia.org/wiki/Nuclear_fusion#Requirements

Good explanation, the only thing i'd say is that binding energy per nucleon reaches a maximum for iron, obviously the bigger the nucleus, the more nucleons and the higher the binding energy.

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/imgnuk/bcurv.gif

Mass of nucleus = Z Mp + N Mn - B/c^2

Mass of daughter nuclei = (Z1 Mp + N1 Mn - B1/c^2) + (Z2 Mp + N2 Mn - B2/c^2) = Z Mp + N Mn - B1/c^2 - B2/c^2

Where Mp, Mn are the masses of the proton and neutron, Z and N are the number of protons and neutrons and B is the binding energy.

If a heavy element fissions you obtain two daugher nuclei with approximately the same combined number of protons and neutrons (Z1 + Z2 = Z, N1 + N2 = N). From the graph, the binding energy per nucleon for both fission products will be higher. Therefore the total masses of the daughter nuclei will be lower, as you are subtracting the binding energies. This missing mass is converted to energy, and it is obvious from the formula E=mc^2 that a small amount of mass gives a huge amount of energy.

This is not strictly true as the nucleus normally fissions to two different daughter nuclei plus a few slow neutrons, but the principle is correct.

[rabbit boy]

Good explanation, the only thing i'd say is that binding energy per nucleon reaches a maximum for iron, obviously the bigger the nucleus, the more nucleons and the higher the binding energy.

Okay, I changed it.

[ikon]

"nucleus normally fissions to two different daughter nuclei plus a few slow neutrons."

ok but is there alpha decay in the nuclear fission (?) lol

[Mathematics]

"nucleus normally fissions to two different daughter nuclei plus a few slow neutrons."

ok but is there alpha decay in the nuclear fission (?) lol

What do you mean? The resulting nuclei are sometimes called daughter nuclei, which can also refer to the decay product from an alpha decay if you're on about the use of that term.