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In what state of matter are particles rigidly fixed in space and held tightly to neighboring particles?

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solids

As shown in Figure above , each state of matter looks quite different at the molecular level. In the case of liquids and solids, the distances between particles are negligible relative to the size of each particle; they are essentially in direct contact with one another. In liquids, particles are free to move and exchange neighbors, resulting in the properties of a fluid. In solids, they are rigidly fixed in space and held tightly to neighboring particles.

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