Respuesta :
Explanation:
1) Edge length of the metal in BCC unit cell = [tex]a=0.33226 nm[/tex]
Atomic radius of the metal atom = r
For BCC unit cell, relationship between edge length and radius is given as:
[tex]r=\frac{\sqrt{3}}{4}\times a=0.4330a[/tex]
[tex]r=0.4330\times 0.33226 nm=0.144 nm[/tex]
[tex]1 nm=10^{-7} cm[/tex]
[tex]r=0.144 nm=0.1439\times 10^{-7} cm=1.44\times 10^{-8} cm[\tex]
The atomic radius of the metal atom in BCC unit cell is [tex]1.44 \times 10^{-8} cm[/tex].
2) Edge length of the metal in FCC unit cell = [tex]a=4.3992 \AA[/tex]
Atomic radius of the metal atom = r
For FCC unit cell, relationship between edge length and radius is given as:
[tex]r=\frac{1}{2\sqrt{2}}\times a=0.3535a[/tex]
[tex]r=0.3535\times 4.3992 \AA=1.56 \AA[/tex]
[tex]1 \AA=10^{-8} cm[/tex]
[tex]1.56\AA=1.56 \times 10^{-8} cm[/tex]
The atomic radius of the metal atom in FCC unit cell is [tex]1.56 \times 10^{-8} cm[/tex].
