The density of chromium metal is 7.2 g `cm^(-3)`. If the unit cell has edge length of 289 pm, determine the type of unit cell. Also, calculate the radius of an atom of chromium. (Atomic mass of chromium = 52 a.m.u.)

Explanation

According to the given data :
Density of chromium metal, d= 7.2 g `cm^(-3)`
Edge length, a = 289 pm= `289 xx 10^(-10)`cm
Atomic mass of chromium, M = 52 g `mol^(-1)`
`d=(Z xx M)/(a^3 xx N_A)= (Z xx (52 g mol^(-1)))/((289 xx 10^(-10) cm)^3 xx (6.022 xx 10^(23) mol^(-1)))` or `Z=(7.2 cm^(-3) xx (289 xx 10^(-10)cm)^3 xx (6.0.22 xx 10^(-23) mol^(-1)))/((52 g mol^(-1)))` = 2.01
Therefore, chromium has bcc lattice
For bcc lattice, `r =(sqrt3)/(4) xx a =(1.732)/(4) xx 289` pm = 125.14 pm