A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in the fusion reacti

Question

A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (given 1 u = 931 MeV)

Accepted Answer

1. **Calculate Total Energy Released (E):** The energy released is equivalent to the mass defect ($\Delta m$) according to the relation $E = \Delta m c^2$. Using the conversion factor provided (1 u = 931 MeV):
   $$ E = 0.02866 	ext{ u} 	imes 931 	ext{ MeV/u} \approx 26.68 	ext{ MeV} $$
2. **Identify Number of Nucleons (A):** The fusion of hydrogen into helium involves four hydrogen nuclei (protons) combining to form one helium nucleus (${}_{2}^{4}\mathrm{He}$) . The mass number ($A$) of the resulting helium nucleus is 4.
3. **Calculate Energy per Nucleon:**
   $$ E_{	ext{per nucleon}} = \frac{	ext{Total Energy}}{	ext{Mass Number}} $$
   $$ E_{	ext{per nucleon}} = \frac{26.68 	ext{ MeV}}{4} \approx 6.67 	ext{ MeV} $$
   This value is closest to option 6.675 MeV.

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