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.

Answer

5

Explanation

`d=(n xx M)/(N_(A) xx a^(3))` or `n=(d xx N_(A) xx a^(3))/M`
`rArr n=2`
Therefore Metal crystallizes in bcc structure and for a bcc lattice `sqrt(3a) = 3r`
`r=sqrt(3)/4 a = (sqrt(3) xx 5)/4 = 2.165 Å = 216.5` pm
`x=216.5/43.3`
x=6