Question

If $M_0$ is the mass of an oxygen isotope ${}_8{O}^{17},M_p$ and $M_n$ are the masses of a proton and a neutron, respectively, then the nuclear binding energy of the isotope is

• A. $(M_o-8M_p)c^2$
• B. $(M_o-8M_p-9M_n)c^2$
• C. $M_o{c}^2$
• D. $(M_o-17M_n)c^2$

Answer 1

The correct option is B $(M_o-8M_p-9M_n)c^2$

$\begin{array}{cc}{M}_0& =\text{mass of}{}_8{O}^{17}\\ M_p& =\text{Mass of proton}\\ M_n& =\text{Mass of neutron}{}^{}\end{array}$

$\text{Binding energy}=\text{mass defect}\left(\Delta m\right)\times c^2$

$\begin{array}{c}\Delta m=(\text{Mass of Oxygen}-\text{total mass of}\text{protons}-\text{total mass of}\text{neutrons}\\ \text{Binding energy}=(M_0-8M_p-9M_n)c^2\end{array}$