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

step 1 Solving part A of this problem. So first writing the reaction 1 -1 -H plus 2 -1 -H gives A -ZX.

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

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

Key Concepts

Reaction Product Identification in Fusion

Identifying the reaction product in a fusion reaction involves applying conservation laws, such as conservation of nucleon number and charge. By combining the nucleons of the reacting species, one determines the mass and charge of the product nucleus. This step is crucial in understanding the energy balance and reaction mechanism in fusion processes.

Quantum Tunneling

Quantum tunneling is a phenomenon where particles can pass through an energy barrier even if they do not possess enough kinetic energy to overcome it classically. In nuclear fusion, tunneling allows for a small probability that nuclei at lower energies can fuse, though this probability is extremely low at room temperature, making such reactions highly unlikely under normal conditions.

Nuclear Fusion

Nuclear fusion is the process in which two light atomic nuclei combine to form a heavier nucleus. This process releases energy because of the difference between the binding energies of the reactants and the product, and it is the primary mechanism that powers stars. It requires conditions of extremely high temperature and pressure to overcome the repulsive forces between the positively charged nuclei.

Binding Energy

Binding energy is the energy required to break a nucleus into its constituent protons and neutrons. It is an indicator of the nucleus's stability; nuclei with higher binding energy per nucleon are generally more stable. In fusion reactions, the difference in binding energy between the reactants and the product is released, often as kinetic energy or electromagnetic radiation.

Coulomb Barrier

The Coulomb barrier is the energy barrier due to the electrostatic repulsion between positively charged nuclei. In order for fusion to occur, the interacting nuclei must have enough kinetic energy to overcome this barrier. This is why high temperatures are necessary in fusion environments, as they provide the requisite energy for the nuclei to come sufficiently close for the strong nuclear force to take effect.

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