a$)$ Determine the unit edge length, $a,$ in nm using the atomic radius. $(6$ pts$)$ You are studying a new pure metal, Alabamium. You have already determined some information:

Name: Alabamium

Symbol: Ab

Atomic Number: $24$

Atomic Weight: $52\frac{g}{m}ol$

Atomic Radius: $0\mathrm{.}128$ nm

Lattice Parameter: $0\mathrm{.}296$ nm

Based on the relationship between the lattice parameter and the atomic radius, which of the following

three cubic crystal structures $($Simple cubic, BCC$,$ FCC$)$ would you predict this material to have? $(6$ pts $)$

Calculate the packing factor for the material? $(6$ pts $)2.$B$3$ MACROSTRUCTURE $(16$ points$)$

A thin cylindrical plate made of iron is approximately $0\mathrm{.}05$ inch thick $(2$ mm $)$ and has a radius of $10$ mm $.$

Assume that all unit cells of the iron plate are arranged so that $"$a$"$ is perpendicular to the plate surface.

The atomic radius of iron is $0\mathrm{.}124$ nm $.$ Assume the temperature is room temperature $(25C).$

b$)$ Calculate the theoretical density and compare it to the measured density provided $(10$ pts$)$

$($a$)$ What is the crystal structure for iron? $(4$ pts$)$ HINT: Look this up online

$($b$)$ Determine the lattice parameter for iron? $(4$ pts$)$

$($c$)$ Determine the total number of unit cells in the plate? $(4$ pts$)$

$($d$)$ State the thickness of the plate in number of unit cells? $(4$ pts$)$