NEET Physics Nuclear Physics And Radioactivity NEET PYQ-Nuclear Physics

\[{{M}_{p}}\] 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.                                                                        [AIPMT (S) 2004]    The mass \[M(N,\text{ }Z)\] of the nucleus is given by :

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

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

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

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

Correct Answer: C

Solution :

Binding energy of a nucleus containing N neutrons and Z protons is

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

\[\Rightarrow \] \[\frac{B}{{{c}^{2}}}=N{{M}_{n}}+Z{{M}_{p}}-M(N,Z)\]

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