Answer:
(a) A = [tex]3.90 \AA[/tex]
(b) [tex]A = 4.50 \AA[/tex]
(c) [tex]A = 5.51 \AA[/tex]
(d) [tex]A = 9.02 \AA[/tex]
Solution:
As per the question:
Radius of atom, r = 1.95 [tex]\AA = 1.95\times 10^{- 10} m[/tex]
Now,
(a) For a simple cubic lattice, lattice constant A:
A = 2r
A = [tex]2\times 1.95 = 3.90 \AA[/tex]
(b) For body centered cubic lattice:
[tex]A = \frac{4}{\sqrt{3}}r[/tex]
[tex]A = \frac{4}{\sqrt{3}}\times 1.95 = 4.50 \AA[/tex]
(c) For face centered cubic lattice:
[tex]A = 2{\sqrt{2}}r[/tex]
[tex]A = 2{\sqrt{2}}\times 1.95 = 5.51 \AA[/tex]
(d) For diamond lattice:
[tex]A = 2\times \frac{4}{\sqrt{3}}r[/tex]
[tex]A = 2\times \frac{4}{\sqrt{3}}\times 1.95 = 9.02 \AA[/tex]
