Calculating Binding Energy of 24 Mg

[rogersj]

I'm trying to figure out the binding energy of 24 Mg. That is (12 protons and 12 neutrons. I keep getting a negative number. Using the equation:
Eb (MeV) = (ZMp + NMn - Ma)931.494 MeV/u I should be able to get the right answer but my mass defect ( delta m) is negative. What am I missing?
Thank you very much.

 

[Doc Al]

You must be plugging in the wrong numbers. Your equation is correct. Since the proton and neutron massess are greater than 1u, and the mass of Mg is less than 24u, the binding energy is positive (as it better be).

Show the us the numbers.

And welcome to Physics Forums, by the way!

 

[rogersj]

got it

thanks!
yeah I got the answer, apparently I wasn't taking into account the coulomb repulsion effect. I did a little reading and found this equation:

Eb = C1(A) - C2(A^2/3) - C3 Z(Z-1)/A^1/3 - C4(N-Z)^2/ A

where C1 = 15.7 MeV, C2 = 17.8 MeV, C3 = 0.71 MeV, C4 = 23.6 MeV

I don't quite understand it, but it worked to find the right answer. Thanks for your reply.

 

[swansont]

thanks!
yeah I got the answer, apparently I wasn't taking into account the coulomb repulsion effect. I did a little reading and found this equation:

Eb = C1(A) - C2(A^2/3) - C3 Z(Z-1)/A^1/3 - C4(N-Z)^2/ A

where C1 = 15.7 MeV, C2 = 17.8 MeV, C3 = 0.71 MeV, C4 = 23.6 MeV

I don't quite understand it, but it worked to find the right answer. Thanks for your reply.

You should get the same answer using the mass defect, as Doc Al said. It takes into account all of the interactions without modeling them; it's just a direct measurement of the energy difference.

 

[garytse86]

what is the proper definition of binding energy? Is it also called negative potential energy?