A metal having atomic weight 75 u crystallizes in a cubic unit cell having edge length `5 dotA`. If the density is 2 g `cm^(-3)`, then the radius of the metal atom is_____pm.
`[N_A = 6.0 xx 10^(23) mol^(-1), sqrt(3) = 1.7`]

Answer

`2.125`

Explanation

`"density"=(z_"eff" xx M_"wt")/(a^3 xx N_A)`
`2=(z_"eff" xx 75)/((5 xx 10^-8) xx 6.023 xx 10^(23))`
`z_"eff"=2`
The unit cell is therefore BCC
`r=(sqer3 a)/4=(1.7 xx 5)/4=2.125 dotA`