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Question 44

Assuming the experimental mass of $$^{12}_{6}C$$ as 12 u, The mass defect of $${}^{12}\text{C}$$ atom is (in MeV/$$c^2$$) :
(Mass of proton  = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5$$ $$MeV/$$c^2$$ and c is the speed of the light in vacuum).

$$\Delta m = [Z \cdot m_p + (A - Z) \cdot m_n] - M_{\text{actual}}$$

$$m_{\text{nucleons}} = (6 \times 1.00727 \text{ u}) + (6 \times 1.00866 \text{ u})$$

$$m_{\text{nucleons}} = 6.04362 \text{ u} + 6.05196 \text{ u} = 12.09558 \text{ u}$$

$$\Delta m = 12.09558 \text{ u} - 12 \text{ u} = 0.09558 \text{ u}$$

$$\Delta m = 0.09558 \times 931.5 \text{ MeV}/c^2$$

$$\Delta m \approx 89.03277 \text{ MeV}/c^2 \approx 89.03 \text{ MeV}/c^2$$

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