In order for initially two widely separated deuterons to get close enough to fuse, their kinetic energy must be about a. \(0.1 \mathrm{MeV}\) b. 3 MeV. c. -3 MeV. d. \(0.3 \mathrm{MeV}\)

The Coulomb barrier is an energy threshold that two charged particles, such as atomic nuclei, must overcome to get close enough for a reaction, like nuclear fusion, to occur. This barrier results from the electrostatic force of repulsion between particles with the same electric charge.

In the context of fusion, when two deuterons, with positive charges, approach each other, they experience a repulsive force due to their like charges. This force creates an energy 'hill' they must 'climb' over before they can interact and fuse. The height of this Coulomb barrier is a pivotal concept; it's essentially the minimum kinetic energy the particles must possess to overcome the electrostatic repulsion.

The magnitude of the Coulomb barrier depends on factors such as the charge magnitude of the particles and the distance between their centers, which is linked to their radii. As such, the barrier is specific to the particles involved, being higher for particles with larger charges and smaller separations.

Kinetic energy plays a fundamental role in nuclear fusion. For two nuclei to fuse, they must collide with sufficient energy to overcome the Coulomb barrier, the energy hurdle presented by their electrostatic repulsion.

In the world of subatomic particles, temperature is a measure of kinetic energy. The hotter the plasma in which these particles exist, the faster they move, and the greater their kinetic energy. Therefore, a high enough temperature, which equates to high kinetic energy, can enable the particles to get close enough for the strong nuclear force to take over, pulling the nuclei together to initiate fusion.

The necessary kinetic energy must be precise; too low, and the nuclei cannot overcome their mutual repulsion; too high, and it may lead to unnecessary energy expenditure or other unintended reactions. Calculations and experiments therefore strive to find the 'goldilocks' zone of kinetic energy that facilitates an efficient fusion process.

The deuteron is the nucleus of a deuterium atom, which is an isotope of hydrogen. Unlike the most common hydrogen nucleus that consists of just one proton, a deuteron comprises one proton and one neutron. This difference is crucial in nuclear fusion reactions.

In terms of charge, the deuteron carries a positive charge equal to the elementary charge due to its single proton. However, its neutron remains neutral, contributing to the mass without affecting the charge. The structure of deuterons influences their behavior in fusion reactions; their mass and charge affect the kinetic energy they require to overcome the Coulomb barrier and the strength of the nuclear force that can bind them once they are within a suitable range.

While the neutron doesn't add charge, it does add to the binding energy of the nucleus, thereby affecting the energy release during fusion. Understanding the deuteron's structure lays the groundwork for comprehending more complex nuclear reactions and their potential for energy generation.