A) \[M(A,Z)=Z{{M}_{p}}+(A-Z){{M}_{n}}-BE/{{c}^{2}}\]
B) \[M(A,Z)=Z{{M}_{p}}+(A-Z){{M}_{n}}+BE\]
C) \[M(A,Z)=Z{{M}_{p}}+(A-Z){{M}_{n}}-BE\]
D) \[M(A,Z)=Z{{M}_{p}}+(A-Z){{M}_{n}}-BE/{{c}^{2}}\]
Correct Answer: D
Solution :
Binding energy of a nucleus containing N neutrons and Z protons is |
\[BE=[N{{M}_{n}}+Z{{M}_{p}}-M(A,Z)]{{c}^{2}}\] |
\[\Rightarrow \] \[\frac{BE}{{{c}^{2}}}=N{{M}_{n}}+Z{{M}_{p}}-M(A,Z)\] |
\[\Rightarrow \] \[\frac{BE}{{{c}^{2}}}=(A-Z){{M}_{n}}+Z{{M}_{p}}-M(A,Z)\] |
(as \[N=A-Z\]) |
\[\Rightarrow \]\[M(A,Z)=Z{{M}_{p}}+(A-Z){{M}_{n}}-BE/{{c}^{2}}\] |
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