Based on the description of gallium melting in the person's hand, the correct changes that occur on a microscopic level would be:
A. The gallium atoms will gain kinetic energy. B. The gallium atoms will be moving faster on average. C. The gallium atoms will increase in temperature.
All three of these options are related to the process of melting, where the increase in temperature leads to greater kinetic energy and faster movement of the atoms.
Option D is somewhat misleading; while the gallium atoms do move more freely in the liquid state, the term "gain potential energy" isn't typically used in this context. Instead, they gain kinetic energy and become less arranged than they are in the solid state.
Therefore, options A, B, and C are correct regarding the changes that occur on a microscopic level as gallium melts in the hand.