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## QuestionPhysicsClass 12

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 $$\mathit{MeV}/c^2$$ .

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 $$127.5\mathit{MeV}/c^2$$ .