When gallium melts in a person's hand, the following changes occur on a microscopic level:
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The gallium atoms will gain kinetic energy. - As the temperature increases, the kinetic energy of the gallium atoms increases, causing them to move more vigorously.
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The gallium atoms will increase in temperature. - The heat from the person's hand transfers to the gallium, raising its temperature which is a measure of the average kinetic energy of the atoms.
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The gallium atoms will gain potential energy, moving freely from each other. - As solid gallium melts into liquid, the potential energy of the atoms increases because they overcome intermolecular forces that keep them in fixed positions.
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The gallium atoms will be moving faster on average. - With increased kinetic energy, the atoms in the liquid state will indeed move faster on average compared to the solid state, where they are more constrained.
In summary, all of these changes reflect the transition of gallium from a solid to a liquid state due to the absorption of heat energy. However, if we are to select one primary change regarding the microscopic behavior of gallium atoms during melting, "The gallium atoms will gain kinetic energy" is a key observation related specifically to the transition from solid to liquid.