Question

Chromium has a BCC crystal structure, an atomic radius of 0.125 nm, and an atomic weight of 52.00 g/mol. Compute its theoretical density and compare it with the experimental value found inside the front cover. (For those without the text, this value is 7.19 g/cm3

Answer 1

Atomic mass of chromium is M = 52.0 g/mol

Number of atoms in BCC crystal lattice, Z = 2 atoms

Atomic radius of BCC

$r = \frac{\sqrt{3}a}{4}$

$0.125 \;nm = \frac{\sqrt{3}a}{4}$

$0.125 \times 10^{-7} \;cm = \frac{\sqrt{3}a}{4}$

$a = \frac{0.125 \times 10^{-7} \times 4}{\sqrt{3}} = 0.289 \times 10^{-7}\;cm$

Density of chromium

$D = \frac{ZM}{a^3N}$

$D = \frac{2 \times 52.0}{(0.289 \times 10^{-7})^3 \times 6.023 \times 10^{23}} = 7.15 \;g/cm^3$