If $M_{O}$ 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, the nuclear binding energy of the isotope is

M_{O} c^{2}

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(M_{O} - 17 M_{n}) c^{2}

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(M_{O} - 8 M_{p}) c^{2}

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(8 M_{p} + 9 M_{n} - M_{O}) c^{2}

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Solution

The correct option is D $(8 M_{p} + 9 M_{n} - M_{O}) c^{2}$
Nuclear binding energy of a nucleus is given by ,
$B . E = Δ m c^{2} =$ (mass of nucleons-mass of nucleus) $c^{2}$
where $Δ m =$ mass defect
Number of protons in $_{8} O^{17}$ , $p = 8$
Number of neutrons in $_{8} O^{17}$ , $n = 17 - 8 = 9$
Hence , binding energy of $_{8} O^{17}$ ,
$B . E . = (8 M_{p} + 9 M_{n} - M_{O}) c^{2}$

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