(A) The binding energy $(B.E.)$ of a nucleus is the energy equivalent of the mass defect $(\Delta m)$.The mass defect is defined as the difference bet

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$B.E. = [Z M_p + (A - Z) M_n - M(A, Z)] c^2$

(A) The binding energy $(B.E.)$ of a nucleus is the energy equivalent of the mass defect $(\Delta m)$.The mass defect is defined as the difference between the sum of the masses of individual nucleons (protons and neutrons) and the actual mass of the nucleus.Number of protons = $Z$Number of neutrons = $A - Z$Mass defect $\Delta m = [Z M_p + (A - Z) M_n - M(A, Z)]$According to Einstein's mass-energy equivalence principle, $B.E. = \Delta m c^2$.Therefore, $B.E. = [Z M_p + (A - Z) M_n - M(A, Z)] c^2$.

Class 12 Physics Nuclei Mass-Energy, Nuclear Binding Energy, Nuclear Stability

Medium

$A$ nucleus $^{A}_{Z} X$ has mass represented by $M(A, Z)$. If $M_p$ and $M_n$ denote the mass of a proton and a neutron respectively, and $B.E.$ is the binding energy in $MeV$, then:

AIPMT 2007 All AIPMT

A
$B.E. = [Z M_p + (A - Z) M_n - M(A, Z)] c^2$
B
$B.E. = [Z M_p + A M_n - M(A, Z)] c^2$
C
$B.E. = M(A, Z) - Z M_p - (A - Z) M_n$
D
$B.E. = [M(A, Z) - Z M_p - (A - Z) M_n] c^2$

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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 a proton and a neutron respectively, and $B.E.$ is the binding energy in $MeV$, then:

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