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A nucleus $^{A}_{Z}X$ has mass represented by $M(A, Z)$. If $M_p$ and $M_n$ denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then
A
B.E. $= [ZM_p + (A - Z)M_n - M(A, Z)]c^2$
B
B.E. $= [ZM_p + ZM_n - M(A, Z)]c^2$
C
B.E. $= M(A, Z) - ZM_p - (A - Z)M_n$
D
B.E. $= [M(A, Z) - ZM_p - (A - Z)M_n]c^2$
Detailed Solution
A nucleus $^{A}_{Z}X$ contains $Z$ protons and $(A - Z)$ neutrons.
The difference between the total mass of the constituents and the mass of the nucleus, $\Delta M$, is called the mass defect:
$\Delta M = [ZM_p + (A - Z)M_n] - M(A, Z)$
The binding energy is the energy equivalent of the mass defect: B.E. $= \Delta M c^2$
B.E. $= [\{ZM_p + (A - Z)M_n\} - M(A, Z)]c^2$
The mass of the nucleus is less than the sum of the masses of its nucleons, so this quantity is positive.
The difference between the total mass of the constituents and the mass of the nucleus, $\Delta M$, is called the mass defect:
$\Delta M = [ZM_p + (A - Z)M_n] - M(A, Z)$
The binding energy is the energy equivalent of the mass defect: B.E. $= \Delta M c^2$
B.E. $= [\{ZM_p + (A - Z)M_n\} - M(A, Z)]c^2$
The mass of the nucleus is less than the sum of the masses of its nucleons, so this quantity is positive.