Consider the fusion reaction of a proton and a deuteron: ^1 H+1^2 H →X . (a) Identify the reacti

step 1 For this question, we are looking at the reaction or the fusion of a proton on the left with a d

Consider the fusion reaction of a proton and a deuteron: ^1...

Consider the fusion reaction of a proton and a deuteron: $^{1} \mathrm{H}+_{1}^{2} \mathrm{H} \rightarrow \mathrm{X} .$ (a) Identify the reaction product $\mathrm{X}$. (b) The binding energy of the deuteron is about $1.1 \mathrm{MeV}$ per nucleon and the binding energy of "X" is about 2.6 MeV per nucleon. Approximately how much energy (in MeV) is released in this fusion reaction? (c) Why is this reaction unlikely to occur in a room temperature setting?

Key Concepts

Nuclear Fusion

Nuclear fusion is the process by which two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This energy release stems from the mass difference between the reactants and the fusion product, according to the mass-energy equivalence principle. The process is fundamental to energy production in stars and is a major focus of controlled fusion research on Earth.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. A higher binding energy per nucleon indicates a more stable nucleus. In fusion reactions, the differences in binding energy between the reactants and products explain the net energy produced, as the formation of a more tightly bound nucleus releases energy.

Q-Value of a Reaction

The Q-value of a nuclear reaction is the net amount of energy released or absorbed during the reaction. Calculated from the differences in binding energies of the reactants and products, a positive Q-value indicates that energy is released. This concept is essential in determining the overall energetics of fusion reactions.

Coulomb Barrier

The Coulomb barrier is the energy barrier due to electrostatic repulsion between two positively charged nuclei. For fusion to occur, the interacting nuclei must have sufficient kinetic energy to overcome this repulsive force, or rely on quantum tunneling, albeit with low probability at low energies.

Thermal Energy and Reaction Rates

At room temperature, the thermal kinetic energy of particles is far too low to overcome the Coulomb barrier between nuclei. This low energy results in an extremely small probability for fusion reactions to occur, making such reactions practically impossible under normal conditions.

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