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Find the energy equivalent of one atomic mass unit, first in Joules and then in \(\mathit{MeV}\) . Using this, express the mass defect of \({_8^{16}}{{}}{{}}{O}{}\)  in \(\mathit{MeV}/c^2\) .

Answer

One atomic mass unit is \(1u=1.6605\times 10^{-27}\mathit{kg}\) .
The mass, \(m=1.6605\times 10^{-27}\mathit{kg}\) .
The speed of light, \(c=3\times 10^8m/s\)
Convert one atomic mass unit into energy E as follows:
\(E=mc^2\)
\(E=(1.6605\times 10^{-27})\times \left(3\times 10^8\right)^2J\)
\(E=1.4924\times 10^{-10}J\times \frac{10^6\mathit{MeV}}{1.602\times 10^{-19}J}\)
\(E=931.5\mathit{MeV}\)
\(1u=931.5\mathit{MeV}/c^2\)
For \({_8^{16}}{{}}{{}}{O}{}\) , \({\Delta}M=0.13691u\)
\({\Delta}M=0.13691\times 931.5\mathit{MeV}/c^2\)
\({\Delta}M=127.5\mathit{MeV}/c^2\)
Hence, the energy needed to separate \({_8^{16}}{{}}{{}}{O}{}\)  into its constituents is \(127.5\mathit{MeV}/c^2\) .
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