The edge length of unit cell of a metal `(Mw = 24)` having cubic structure is `4.53 Å`. If the density of metal is `1.74 g cm^(-3)`, the radius of metal is `(N_(A) = 6 xx 10^(23))`

Options

A. `180` pm
B. `160` pm
C. `140` pm
D. `190` pm

Answer

B

Explanation

`rho = (Z_(eff) xx Mw)/(.a^(3) xx N_(A))`
`1.74 g cm^(-3) = (Z_(eff) xx 24)/((4.53 xx 10^(8))^(3) cm^(3) xx 6 xx 10^(23)"atoms")`
`:. Z_(eff) = 4` (fcc structure)
For fcc, the radius of atom is.
`r = (a)/(2sqrt(2)) = (4.53Å)/(2sqrt(2)) = 1.60Å = 160 "pm"`