Question

An element crystallizes in a structure having FCC unit cell of an edge length $200$ pm. Calculate the density (in g cm${}^{-3}$) if $200$ grams of it contains $24\times {10}^{23}$ atoms.

• A. $41.6$
• B. $42.6$
• C. $43.6$
• D. $44.6$

Answer 1

The correct option is A $41.6$

The formula of density is as follows:

$d=\frac{z\times w}{N\times a^3}$

For FCC unit cell, $z=4$

$N=24\times {10}^{23}$ atoms

$a=200pm=2\times {10}^{-8}cm$

Now,

$d=\frac{4\times 200}{24\times {10}^{23}\times 8\times {10}^{-24}}$

$=\frac{1000}{24}$

$x=41.67g.c{m}^{-3}$