Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are $_{1}^{1} \mathrm{H}, \quad 1.00782\( u; \)_{1}^{2} \mathrm{H}, \quad 2.01410 \quad \mathrm{u} ;$ and an electron, \(5.4858 \times 10^{-4}\) u. (Hint: Think carefully about how to account for the electron mass.) $$ _{1}^{1} \mathrm{H}+_{1}^{1} \mathrm{H} \longrightarrow_{1}^{2} \mathrm{H}+_{+1}^{0} \mathrm{e} $$

The energy released per gram of hydrogen nuclei reacted for the given nuclear reaction can be found by: 1. Calculate the mass of reactants (\(2 \times 1.00782\) u) and products (\(2.01410 + 5.4858 \times 10^{-4}\) u). 2. Find the mass difference between reactants and products (∆m) (\(2 \times 1.00782 - (2.01410 + 5.4858 \times 10^{-4})\)). 3. Convert ∆m from atomic mass units (u) to kilograms (kg) using the conversion factor 1 u = \(1.660539 \times 10^{-27}\) kg. 4. Calculate the energy released (E) from the mass difference using Einstein's mass-energy equivalence formula: \(E = ∆m \times c^2\), where \(c = 3 \times 10^8 m/s\) is the speed of light. 5. Convert the mass of hydrogen nucleus to grams using the conversion factor 1 u = \(1.660539 \times 10^{-24}\) g. 6. Calculate the energy released per gram of hydrogen nuclei reacted by dividing E by the total mass of 2 hydrogen nuclei in grams: \(\text{Energy per gram} = \frac{E}{2 \times m_{\text{H}} \text{(in g)}}\). This process will give you the energy released per gram of hydrogen nuclei reacted for the given nuclear reaction.