Consider the fusion reaction 1^2 H+ 1^2 H → 2^3 He+ 0^1 n . (a) Estimate the barrier energy by

step 1 solving party of this problem. So energy barrier, let it be eB, an energy barrier is equal to re

Consider the fusion reaction 1^2 H+ 1^2 H → 2^3 He+ 0^1 n ....

Consider the fusion reaction ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n} .$ (a) Estimate the barrier energy by calculating the repulsive electrostatic potential energy of the two ${ }_{1}^{2} \mathrm{H}$ nuclei when they touch. (b) Compute the energy liberated in this reaction in $\mathrm{MeV}$ and in joules. (c) Compute the energy liberated per mole of deuterium, remembering that the gas is diatomic, and compare with the heat of combustion of hydrogen, about $2.9 \times 10^{5} \mathrm{~J} / \mathrm{mol}$

Key Concepts

Coulomb Barrier

The Coulomb barrier refers to the energy barrier arising from the electrostatic repulsion between two positively charged nuclei. To achieve fusion, the nuclei must overcome this repulsion, typically requiring high kinetic energy or other quantum mechanical effects to allow the nuclei to come close enough for the strong nuclear force to act, thereby enabling fusion.

Nuclear Fusion Reaction

This concept involves the process where two light atomic nuclei combine to form a heavier nucleus, typically releasing energy due to the difference in binding energy between the reactants and the product. In the context of the given problem, a deuterium-deuterium fusion reaction is considered, which is one of several fusion reactions studied in nuclear physics and astrophysics.

Electrostatic Potential Energy

This is the energy due to the repulsive or attractive forces between charged particles, calculated using Coulomb's law. In nuclear fusion problems, it is used to estimate the barrier energy that must be overcome for the nuclei to come into close contact, which is crucial in understanding the conditions required for fusion to occur.

Energy Release in Nuclear Reactions

This concept deals with the energy produced or required during a nuclear reaction, derived from the mass defect (the difference in mass between reactants and products) according to Einstein’s mass-energy equivalence principle (E=mc²). It is essential for evaluating the net gain or loss of energy in reactions such as fusion and is typically expressed in units like megaelectronvolts (MeV) or joules.

Molar Energy Calculations

Molar energy calculations involve determining the energy change per mole of reactant, which is useful for comparing nuclear energy releases with chemical processes, such as the combustion of hydrogen. This concept bridges nuclear and chemical energetics by scaling single-event energy changes to macroscopic quantities that can be measured in laboratory settings.

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