Chromium metal crystallizes with a body-centred cubic lattice. The edge length of the unit cell is found to be 287 pm. Calculate the atomic radius. What would be the density of chromium in g `cm^(-3)` ? (atomic mass of Cr = 52.99)

Explanation

For a body - centred cubic lattic , Z= 2
Edge length , a= 287 pm = `287 xx 10^(-10) cm`
Atomic mass of chromium , M = 52.99 g `"mol"^(-1)`
For bcc lattice , r = `(sqrt3)/(4) xx a`
`=(1.732)/(4) xx a`
`=(1.732)/(4)xx 287 ` pm = 124.27 pm
`d= (Z xx M)/(a^3 xx N_A)`
`=(2xx 52.99 g "mol"^(-1))/((287 xx 10^(-10) cm)^3 xx 6.02 xx 10^(23) "mol"^(-1))`
=7.44 g `"cm"^(-3)`