If $M_{o}$ is the mass of an oxygen isotope ${_{8} O}^{17}, M_{P}, M_{N}$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is (The speed of light is C)

(M_{O} - 8 M_{P}) C^{2}

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(M_{O} - 8 M_{P} - 9 M_{N}) C^{2}

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M_{O} C^{2}

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(M_{O} - 17 M_{N}) C^{2}

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Solution

The correct option is B $(M_{O} - 8 M_{P} - 9 M_{N}) C^{2}$
$\begin{matrix} Given - & * {Mass of}_{8} O^{17} isotope = M_{0} * Mass of neutron = M_{N} * Mass of proton = M_{p} \end{matrix}$

$For the decay of the Isotope we can write-$
$_{8} O^{17} ⟶_{8} O^{16} + H^{+} (Neutron)$
$For the decay of the Isotope we can write-$

$\begin{matrix} B E = Δ m \cdot c^{2} = (M_{Reactant} - M_{product}) \cdot C^{2} B E = (M_{0} - M_{product}) \cdot c^{2} \end{matrix}$

$\begin{matrix} M product \Rightarrow we have 8 protons and 9 neutrons M_{product} = 8 M_{p} + 9 M_{N} \Rightarrow B E = (M_{0} - 8 M_{p} - 9 M_{N}) \cdot c^{2} \end{matrix}$

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