If M(A, Z),M_p,and M_n represent the masses o | vedclass

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Question

(A) The binding energy $(BE)$ is the energy equivalent to the mass defect $(\Delta m)$,which is the difference between the total mass of the constitue

Vedclass · Accepted Answer

$M(A, Z) = ZM_p + (A-Z)M_n - BE/c^2$

Vedclass · Answer

(A) The binding energy $(BE)$ is the energy equivalent to the mass defect $(\Delta m)$,which is the difference between the total mass of the constituent nucleons and the actual mass of the nucleus.The mass defect is given by $\Delta m = [ZM_p + (A-Z)M_n] - M(A, Z)$.According to Einstein's mass-energy equivalence principle,$BE = \Delta m 	imes c^2$.Substituting the expression for $\Delta m$,we get $BE = [ZM_p + (A-Z)M_n - M(A, Z)] 	imes c^2$.Dividing by $c^2$,we have $BE/c^2 = ZM_p + (A-Z)M_n - M(A, Z)$.Rearranging the terms to solve for $M(A, Z)$,we get $M(A, Z) = ZM_p + (A-Z)M_n - BE/c^2$.Thus,the correct relation is $M(A, Z) = ZM_p + (A-Z)M_n - BE/c^2$.

If $M(A, Z)$,$M_p$,and $M_n$ represent the masses of the nucleus ${}_{Z}^{A}X$,proton,and neutron in $u$ units respectively $(1u = 931.5 \, MeV/c^2)$,and $BE$ represents the binding energy in $MeV$,then which of the following relations is correct?

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