Chromium metal crystallizes with a body-centred cubic lattice. The length of the unit cell edge is found to be `287`pm. Calculate the atomic radius. What woulds be the density of chromium in `g cm^(-3)`?

Explanation

In bcc unit cell, ` 4r = sqrt(3)` a
`rArr " " r(Cr) = (sqrt(3)a)/(4) (sqrt(3))/(4) xx 287`pm = 124.3 pm
Density of solid = `(NM)/(N_(A).a^(3))`
N = Number of atoms per unit cell, M = Molar mass
` a^(2)` = Volume of cubic unit cell, ` N_(A)` = Avogadro’s number
`= (2 xx 52 g)/(6.023 xx 10^(23)) xx ((1)/(2.87 xx 10^(-8) cm ))^(3) = 7.3 g // cm^(3)`