Calculate the energy change for the following nuclear...

$ \quad$ Calculate the energy change for the following nuclear reaction (in joules per mole of ${ }_{1}^{2} \mathrm{H}$ ). $$ { }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n} $$ Give the energy change in $\mathrm{MeV}$ per ${ }_{1}^{2} \mathrm{H}$ nucleus. See Table $20.3$.

$ \quad$ Calculate the energy change for the following nuclear reaction (in joules per mole of ${ }_{1}^{2} \mathrm{H}$ ).
$$
{ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}
$$
Give the energy change in $\mathrm{MeV}$ per ${ }_{1}^{2} \mathrm{H}$ nucleus. See Table $20.3$.

Key Concepts

Nuclear Reaction

A nuclear reaction involves changes in an atom's nucleus, where reactants (such as different isotopes of hydrogen in this case) fuse or split to form new nuclei. In the context of energy calculations, understanding the reaction helps to identify which nuclear species are involved and the way mass changes during the process, which is crucial for determining the energy released or absorbed.

Mass Defect

The mass defect is the difference between the total mass of the individual nucleons in the reactants and the total mass of the product nuclei after the reaction. This discrepancy arises because some of the mass is converted into energy, indicating that the mass of a bound system is less than the sum of its parts. It is a key factor in computing the energy change in nuclear reactions.

Mass–Energy Equivalence

Based on Einstein's famous equation E = mc², mass–energy equivalence provides the principle for converting a mass defect into an energy value. This concept is fundamental in nuclear physics, as it explains how the loss of mass in a reaction translates into the enormous amounts of energy observed in nuclear processes.

Binding Energy

Binding energy is the energy required to keep the nucleus intact, or conversely, the energy released when a nucleus is formed from its constituent protons and neutrons. It correlates directly to the mass defect, as nuclei with higher binding energy typically have a greater mass difference compared to their separated nucleons, leading to larger energy releases during nuclear reactions.

Unit Conversions

Unit conversions are critical when expressing the calculated energy change in different units. In nuclear reactions, energy is often expressed in joules per mole or MeV per nucleus. Understanding how to convert between these units, utilizing constants such as Avogadro’s number and the conversion factor between joules and MeV, is essential for presenting the energy change in the desired format.

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