In $\mathrm{M}_{\mathrm{O}}$ is the mass of an oxygen isotope ${ }_8 \mathrm{O}^{17}$ and $M_p$ and $M_N$…

In $\mathrm{M}_{\mathrm{O}}$ is the mass of an oxygen isotope ${ }_8 \mathrm{O}^{17}$ and $M_p$ and $M_N$ are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is
  1. $\quad \mathrm{M}_{\mathrm{o}} \mathrm{C}^2$
  2. $\quad\left(\mathrm{M}_{\mathrm{O}}-8 \mathrm{M}_{\mathrm{p}}\right) \mathrm{C}^2$
  3. $\left(\mathrm{M}_{\mathrm{O}}-17 \mathrm{M}_{\mathrm{N}}\right) \mathrm{C}^2$
  4. $\left(\mathrm{M}_{\mathrm{o}}-8 \mathrm{M}_{\mathrm{p}}-9 \mathrm{M}_{\mathrm{N}}\right) \mathrm{C}^2$

Solution

Number of protons $=8$ Number of neutrons $=17-8=9$ Binding energy, $\begin{aligned} B E & =\left(M_{\text {nucleus }}-M_{\text {nucleons }}\right) C^2 \\ & =\left(M_0-8 M_p-9 M_N\right) C^2 \end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 1)

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