It is possible to make crystalline solids that are only one layer of atoms thick. Such “two-dimensional” crystals can be created by depositing atoms on a very flat surface.
(a) If the atoms in such a two-dimensional crystal can move only within the plane of the crystal, what will be its molar heat capacity near room temperature? Give your answer as a multiple of R and in J/mol· K.
(b) At very low temperatures, will the molar heat capacity of a two dimensional crystal be greater than, less than, or equal to the result you found in part (a)? Explain why.