Nuclei - Result Question 32

33. If $M(A ; Z), M_p$ and $M_n$ denote the masses of the nucleus $ _Z^{A} X$, proton and neutron respectively in units of $u(1 u=931.5 MeV / c^{2})$ and $BE$ represents its bonding energy in $MeV$, then

[2008] (a) $M(A, Z)=ZM_p+(A-Z) M_n-BE / c^{2}$

(b) $M(A, Z)=ZM_p^{p}+(A-Z) M_n+BE$

(c) $M(A, Z)=ZM_p^{p}+(A-Z) M_n-BE$

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

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Answer:

Correct Answer: 33. (a)

Solution:

  1. (a) Mass defect $=ZM_p+(A-Z) M_n-M(A, Z)$

or, $\frac{B . E}{c^{2}}=Z M_p+(A-Z) M_n-M(A, Z)$

$\therefore \quad M(A, Z)=Z M_p+(A-Z) M_n-\frac{B . E \text{. }}{c^{2}}$