Question

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 1

Correct Answer - 216.5 pm (so, the required answer is 217 pm)
`rho=(Zxxm)/(N_(A)V)rArrZ=(rhoN_(Aa^(3)))/(m)=(2xx6xx10^(23)xx(5xx10^(-4)))/(75)approx2`
(Therefore, metal crystallizes in bcc strucutre and for a bcc lattice `sqrte(3)a=4r`)
`r=(sqrt(3)a)/(4)=sqrt(3)/(4)xx5overset(@)A=2165overset(@)A=216.5`pm
(so, the required answer is 217pm)