The unit cell of a metallic element of atomic mass (`108 g //"mole"`) and density `10.5 g//cm^(3)` is a cube with edge length of 409 pm. The structure of the crystal lattice would be:

Answer

Z = 4, fcc

Explanation

`rho = (Z xx M)/(a^3 xx N_A)`
`a = 409 "pm" = 409 xx 10^(-10) cm`
`10.5 = (Z xx 108)/((409 xx 10^(-10))^(3) xx (6.022 xx 10^(23)))`
`:. Z = (10.5 xx (409 xx 10^(-10))^(3) xx (6.022 xx 10^(23)))/(108) = 4.0`
`:. ` fcc type structure .