Question

Chromium crystallizes with a body-centered cubic unit cell. The radius of a chromium atom is 125 pm . Calculate the density of solid crystalline chromium in grams per cubic centimeter.

Answer 1

Answer:

$\rho=7.15\ g/cm^3$

Explanation:

The expression for density is:

$\rho=\frac {Z\times M}{N_a\times {{(Edge\ length)}^3}}$

$N_a=6.023\times 10^{23}\ {mol}^{-1}$

M is molar mass of Chromium = 51.9961 g/mol

For body-centered cubic unit cell , Z= 2

$\rho$ is the density  

Radius = 125 pm = $1.25\times 10^{-8}\ cm$

Also, for BCC, $Edge\ length=\frac{4}{\sqrt{3}}\times radius=\frac{4}{\sqrt{3}}\times 1.25\times 10^{-8}\ cm=2.89\times 10^{-8}\ cm$

Thus,  

$\rho=\frac{2\times \:51.9961}{6.023\times \:10^{23}\times \left(2.89\times 10^{-8}\right)^3}\ g/cm^3$

$\rho=7.15\ g/cm^3$