Rest Mass, Mass Defect and Binding Energy

[MDwannabe7]

In the solution to a problem asking for the mass defect and binding energy of a nucleus, Kaplan states that "the rest energy of 1 amu is 932 MeV, so using E=mc^2 we find that c^2 = 932 MeV/amu." How do they get that and what does it mean?

I understand the mass defect to be the difference between the mass of the nucleus and the mass of the constituent nucleons. This is basically equal and opposite to the binding energy (the energy holding the nucleons together in the nucleus). If I understand rest mass correctly, that is the mass of a particular particle at rest and is based on Einstein's Theory of Relativity that Energy and Mass are inter-convertible.

What I don't understand is how you can just say that the speed of light squared is equal to the rest energy of 1 amu. Does anyone understand this?

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[engineeredout]

In the solution to a problem asking for the mass defect and binding energy of a nucleus, Kaplan states that "the rest energy of 1 amu is 932 MeV, so using E=mc^2 we find that c^2 = 932 MeV/amu." How do they get that and what does it mean?

E = mc^2. Rearrange to form E/m = c^2 = MeV/amu = c^2. For one amu, this means 932 MeV/amu.

eV = 1.6 X 10-19J.

J = kg*(m^2/s^2)

c = m/s = m^2/s^2.

Got it now?

 

[MDwannabe7]

Yes, thank you. Tell me if this is correct:

The atomic mass unit, amu, can be defined as 1/12 the mass of a carbon 12 atom, which is equal to 1.660540x10^-27 kg. Using Einstein's Theory of Relativity, we can determine the energy equivalent of one amu.

E=mc^2; m of 1 amu = 1.660540x10^-27 kg; c = 3.00x10^8 m/s

Plugging these values in gives us the energy equivalent in Joules (a Joule = Newton*Meter = kg*m^2/s^2) = 1.494486x10^-10 J.

Since physicists like to work in eV, 1 eV = 1.6022x10^-19 J. Therefore, if we divide our answer in J by the conversion factor, we get 9.32x10^8 or 932 MeV. Therefore, the energy equivalent of 1 amu is 932 MeV, which can be plugged into the equation above my multiplying the number of amus by 932 MeV.

So, in the problem I was referencing - if 0.02930 amus is the mass defect, then multiplying that by 932 MeV should give me the Binding Energy for that nucleus, right?

 

[futuredoctor10]

So, in the problem I was referencing - if 0.02930 amus is the mass defect, then multiplying that by 932 MeV should give me the Binding Energy for that nucleus, right?

Yep. E=mc^2, where c^2 = 932 MeV. Using this equation with the numbers you provided will yield the binding energy (E) for the nucleus in MeV