Find the binding energy per nucleon (in MeV/nucleon) of carbon-12. Assume:
M_C = 12.000 000 u
M_p = 1.007 825 u
M_n = 1.008 665 u
U = 1.66 *10 ^- ²⁷ kg

Question

Find the binding energy per nucleon (in MeV/nucleon)of carbon-12. Assume: M_C = 12.000 000 u M_p = 1.007 825 u M_n = 1.008 665 u U = 1.66 *10 ^- ²⁷ kg

Quizplus · Accepted Answer

The binding energy of a nucleus is given by
E = [Zmp + (A − Z)mn − M]c^2
where Z is the atomic number, A is the mass number, mp and mn are the masses of the proton and neutron respectively and M is the mass of the nucleus.
For carbon-12:
Z = 6
A = 12
mp = 1.007825 u
mn = 1.008665 u
M = 12.000000 u
Substituting the values, we get
E = [6(1.007825) + 6(1.008665) - 12.000000]c^2
= -92.16 MeV
The binding energy per nucleon is given by
BE/A = E/A
Substituting the values, we get
BE/A = -92.16/12
= -7.68 MeV/nucleon
Taking the absolute value, we get
BE/A = 7.68 MeV/nucleon
Since this is closest to choice D, the answer is D.

Find the Binding Energy Per Nucleon (In MeV/nucleon)of Carbon-12