Question

Silver crystallizes in a fcc lattice and has a density of $10.6$ g cm${}^{-3}$. What is the length (in nm) of an edge of the unit cell?

• A. $0.407$
• B. $0.2035$
• C. $0.101$
• D. $4.07$

Answer 1

The correct option is A $0.407$

The expression for density is as follows:

$d=\frac{ZM}{V{N}_A}⟹a^3=\frac{ZM}{d{N}_A}$

For fcc crystal lattice-

$Z=4$

$Edge=a$

Substituting the values in the above expression, we get-

$a^3=\frac{4\times 108}{10.6\times 6.023\times {10}^{23}}⟹a=4.07\times {10}^{-8}$ cm $=0.407$ nm