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NEET AIPMT SOLVED PAPER SCREENING 2004

  • question_answer
    \[{{M}_{p}}\]denotes the mass of a proton and \[{{M}_{n}}\]that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons.                                                                                                                    The mass M(N, Z) of the nucleus is given by :

    A) \[\text{M}\left( \text{N},\text{ Z} \right)=\text{N}{{\text{M}}_{\text{n}}}+\text{Z}{{\text{M}}_{\text{p}}}-\text{B}{{\text{e}}^{\text{2}}}\]                       

    B) \[\text{M}\left( \text{N},\text{Z} \right)=\text{N}{{\text{M}}_{\text{n}}}+\text{Z}{{\text{M}}_{\text{p}}}+\text{B/}{{\text{c}}^{\text{2}}}\]

    C) \[\text{M}\left( \text{N},\text{ Z} \right)=\text{N}{{\text{M}}_{\text{n}}}+\text{Z}{{\text{M}}_{\text{p}}}-\text{B}/{{\text{c}}^{\text{2}}}\]

    D) \[\text{M}\left( \text{N},\text{ Z} \right)=\text{N}{{\text{M}}_{\text{n}}}+\text{Z}{{\text{M}}_{\text{p}}}+\text{B}/{{\text{c}}^{\text{2}}}\]

    Correct Answer: C

    Solution :

            Binding energy of a nucleus containing N neutrons and Z protons is \[B=[N{{M}_{n}}+Z{{M}_{p}}-M(N,Z)]{{c}^{2}}\] \[\Rightarrow \]       \[\frac{B}{{{c}^{2}}}=N{{M}_{n}}+Z{{M}_{p}}-M(N,Z)\] \[\Rightarrow \]       \[M(N,Z)=N{{M}_{n}}+Z{{M}_{p}}-B/{{c}^{2}}\]


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