Answer:
The classification of the concern is listed in the interpretation segment below.
Explanation:
(a)...
Simple cubic lattice
[tex]a=2r[/tex]
Now,
The unit cell volume will be:
[tex]=a^3[/tex]
[tex]=(2r)^3[/tex]
[tex]=8r^3[/tex]
At one atom per cell, atom volume will be:
[tex]=(1)\times (\frac{4 \pi r^3}{3})[/tex]
Then the ratio will be:
[tex]Ratio=\frac{\frac{4 \pi r^3}{3}}{8r^3}\times 100 \ percent[/tex]
[tex]=52.4 \ percent[/tex]
(b)...
Diamond lattice
The body diagonal will be:
[tex]d=8r=a\sqrt{3}[/tex]
[tex]a=\frac{8}{\sqrt{3}}r[/tex]
The unit cell volume will be:
[tex]=a^1[/tex]
[tex]=(\frac{8r}{\sqrt{3}})^1[/tex]
At eight atom per cell, the atom volume will be:
[tex]=8(\frac{4 \pi r^1}{3})[/tex]
Then the Ratio will be:
[tex]Ratio=\frac{8(\frac{4 \pi r^1}{3})}{(\frac{8r}{\sqrt{3}})^1}\times 100 \ percent[/tex]
[tex]=34 \ percent[/tex]
Note: percent = %
