Question

The different unit cell types have a different packing efficiency. The simple cubic has the least efficient packing and the face-centered cubic has the most efficient packing (sometimes the face-centered cubic is called cubic closest packing). You can determine what percent of the unit cell is occupied by (1) determining the volume of the whole unit cell and (2) determining the volume of the occupied space by the atoms in the unit cell. Remember that the volume of a cube is V

Answer 1

Answer:

The answer is "52.8".

Explanation:

Please find the graph file in the attachment.

They have the atoms in 8 corners with one unit cell in an one so mesh (SCC).

Atoms throughout the corner contribute $\frac{1}{8}$to both the cell unit

Atom number per SCC unit cell, $Z = (8 \times \frac{1}{8}) = 1$

Let 'r' become the atom's radius.  $r = 3.43\times 10^{-8}\ \ cm$

We can see from the diagram that edge length $AB = a = 2r$

$Packing\ efficiency = \frac{(1 \ atom \ Volume \times Z)}{Volume \ of \ unit\ cell \times 100}$

                                 $= \frac{\frac{4}{3}\times \pi \times r^3 \times 1}{a^3 \times 100}\\\\=\frac{\frac{4}{3}\times \pi \times r^3 \times 1}{(2r)^3 \times 100} \\\\=\frac{\frac{4}{3}\times \pi \times( 3.43\times 10^{-8}cm)^3 \times 1}{(2\times 3.43\times 10^{-8}cm)^3 \times 100}\\\\= 52.8 \%$