The edge length of unit cell of a metal having molecular weight `75 g mol^(-1)` is `5 Å` which crystallizes in cubic lattice. If the density is `2 g cc^(-1)`, then find the radius of metal atom `(N_(A) = 6 xx 10^(23))`. Give the answer in pm.

Explanation

`rho = (Z_(eff) xx Mw)/(a^(3) xx N_(A))`
or `2 = (Z_(eff) xx Mw)/((5 xx 10^(-8))^(3) xx 6 xx 10^(23))`
On solving, we get `Z_(eff) ~~ 2`.
This value is for bcc structure.
For bcc,
`r = (sqrt3)/(4)a = (sqrt3)/(4) xx 5 = 2.165 Å = 216.5` pm