What is the Einstein relationship for calculating nuclear binding energy?

[jaredogden]

I was reading over some nuclear physics and I came across the binding energy of a nucleus. The equation is Eb=[ZM(H)+Nm_n-M(^A_ZX)]x931.494 MeV/u

I remember seeing this and using this in class when I took it over a year ago but I can't remember exactly how to use it and I see no examples in the book. If anyone can help explain this that would be awesome. Thanks

 

[Bill_K]

This is really just a definition, the observed mass of a nucleus minus the separate masses of all its protons and neutrons. We don't use it directly for anything, but it tells us something about nuclear forces. Often you'll see a graph of E_b per nucleon. The curve is relatively flat at 8 MeV per nucleon, and this suggests that the nuclear forces 'saturate', acting only between a nucleon and its nearest neighbors. (If each nucleon attracted all the others the binding energy would grow proportionally to N².)

 

[smith345]

Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together. This binding energy can be calculated from the Einstein relationship: