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NEET Physics Nuclear Physics And Radioactivity NEET PYQ-Nuclear Physics

  • question_answer
    If \[M(A,\text{ }Z),\] \[{{M}_{p}}\] and M, denote the masses of the nucleus \[_{Z}^{A}X,\]proton and neutron respectively       in       units      of \[u(1u=931.5MeV/{{c}^{2}})\] and BE represents its binding energy in M                                                                                                                                      [AIPMPT (S) 2008]

    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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