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 binding energy in MeV , then

Correct answer: A. M(A, Z)=Z M_p+(A-Z) M_n-BE / c^2 Binding energy of a nucleus containing N neutrons and Z protons is aligned & BE=[N M_n+Z M_p-M(A, Z)] c^2 & BE c^2 =N M_n+Z M_p-M(A, Z) & BE c^2 =(A-Z) M_n+Z M_p-M(A, Z) & M(A, Z)=Z M_p+(A-Z) M_n-BE / c^2 aligned

NEET 2008

Exam: NEET
Year: 2008
Subject: Physics
Chapter: Nuclear Physics

NEET 2008 · Physics · Nuclear Physics

If M(A, Z), M_P and M_n denote the masses of the nucleus _Z^A X ,...

M(A, Z), M_P and

M_n

denote the masses of the nucleus

{ }_Z^A X

, proton and neutron respectively in units of

\left(1 \mathrm{u}=931.5 \mathrm{MeV} / c^2\right)

and

\mathrm{BE}

represents its binding energy in

\mathrm{MeV}

, then

Options

A $M(A, Z)=Z M_p+(A-Z) M_n-\mathrm{BE} / c^2$
B $M(A, Z)=Z M_p+(A-Z) M_n+\mathrm{BE}$
C $M(A, Z)=Z M_p+(A-Z) M_n-B E$
D $M(A, Z)=Z M_p^P+(A-Z) M_n^n+B E / c^2$

Correct answer

A. $M(A, Z)=Z M_p+(A-Z) M_n-\mathrm{BE} / c^2$

Step-by-step solution

Binding energy of a nucleus containing

N

neutrons and

Z

protons is

\begin{aligned} & \mathrm{BE}=\left[N M_n+Z M_p-M(A, Z)\right] c^2 \\ \Rightarrow & \frac{\mathrm{BE}}{c^2}=N M_n+Z M_p-M(A, Z) \\ \Rightarrow & \frac{\mathrm{BE}}{c^2}=(A-Z) M_n+Z M_p-M(A, Z) \\ \Rightarrow & M(A, Z)=Z M_p+(A-Z) M_n-\mathrm{BE} / c^2 \end{aligned}

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