# Problem: (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?

###### FREE Expert Solution

(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 = 8R2

###### Problem Details

(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?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Atomic Structure concept. You can view video lessons to learn Atomic Structure. Or if you need more Atomic Structure practice, you can also practice Atomic Structure practice problems.