**(a)**

Planar density, PD = number of atoms centered on the plane/ area

For FCC (100):

The number of atoms = (1/4)(4) + 1 = 2

The area of the plane:

$\begin{array}{rcl}\mathbf{A}& \mathbf{=}& {\mathbf{L}}^{\mathbf{2}}\\ & \mathbf{=}& {\mathbf{\left(}\frac{\mathbf{4}\mathbf{R}}{\sqrt{\mathbf{2}}}\mathbf{\right)}}^{\mathbf{2}}\end{array}$

A = 8R^{2}

(a) Derive planar density expressions for (100) in terms of the atomic radius R.

(b) Compute linear density values for the plane for aluminum.

(c) Consider the (100) plane in FCC:

How many atoms are centered on the [100] In FCC?

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