When gallium is melting in a person's hand, several changes occur on a microscopic level:
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The gallium atoms will be moving faster on average: This is correct. As gallium absorbs heat from the hand, the energy causes the atoms to vibrate more rapidly.
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The gallium atoms will gain kinetic energy: This is also correct. As the temperature of the gallium increases, its kinetic energy increases, leading to faster movement of the atoms.
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The gallium atoms will increase in temperature: This statement is true as melting corresponds to an increase in temperature until it reaches the melting point and transitions from solid to liquid.
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The gallium atoms will gain potential energy, moving freely from each other: This is also correct in the context of phase change. As gallium transitions from solid to liquid, the atoms gain potential energy as they overcome the intermolecular forces holding them together in the solid state and become more free to move.
In summary, all four statements reflect changes happening at the microscopic level as solid gallium melts into liquid gallium in a person's hand.