$5.(20)$ Consider a copper crystal, which has the fcc structure, a lattice parameter of $0\mathrm{.}3615$ nm at room temperature, and a coefficient of thermal expansion of $14\mathrm{.}87\backslash$times $10-6\backslash$deg C$-1.$

A$.(5)$ Calculate the interplanar spacing between the $(111)$ set of planes.

B$.(10)$ If illuminated with monochromatic x$-$rays with wavelength $0\mathrm{.}1790$ nm$,$ at what angle will the first$-$order $($n $=1)$ Bragg peaks show up$?$

C$.(5)$ What happens to this angle when the crystal is heated to $500\backslash$deg C and the diffraction angle is measured again?