Q$5.(5$ marks total$)$ X$-$ray diffraction. The first three peaks of an X$-$ray diffraction pattern for a metal

powder sample corresponds to the following $2$ Bragg angles: $40\mathrm{.}58,58\mathrm{.}76,$ and $73\mathrm{.}72.$ The wavelength

of the X$-$ray is $0\mathrm{.}1542$ nm $.$ Using your knowledge about the forbidden reflections in different crystal

systems for metals, determine whether this metal is a BCC or an FCC metal. Additionally, estimate

which metal system is tested.

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