Question

If $M_0$ is the mass of an oxygen isotope ${}_8{\text{O}}^{17}$. $M_P$ and $M_N$ are the mass of a proton and a neutron respectively, the nuclear binding energy of the isotope is

• A. $(M_0-8M_P)c^2$
• B. $M_0{c}^2$
• C. $(M_0-17M_N)c^2$
• D. $(8M_P+9M_N-M_0)c^2$

Answer 1

The correct option is D $(8M_P+9M_N-M_0)c^2$

Binding Energy,

$B.E=\Delta m{c}^2$

Where, $\Delta m\to \text{mass defect}$

For ${}_8{\text{O}}^{17}$, $Z=8;A=17$

$\Rightarrow \Delta m=Z{M}_p+(A-Z)M_N-M_o$

$\Rightarrow B.E=(8M_P+9M_N-M_0)c^2$

Hence, option $\left(B\right)$ is correct.