When gallium is melting in a person's hand, the correct answer is:
the gallium atoms will gain kinetic energy.
As the gallium transitions from a solid to a liquid, the heat from the person's hand increases the kinetic energy of the gallium atoms, causing them to move more freely, which is characteristic of a liquid state. While it is closely related, stating that they gain potential energy is less accurate in this context, as the change from solid to liquid mainly involves an increase in kinetic energy of the atoms.