A element X with atomic mass 60 g/mol has a density of `6.23"g cm"^(-3)`. If the edge length of the unit cell is 400 pm, identify the type of the cubic unit cell. Calculate the radius of the atoms of the element.

Explanation

A=60 g/mol `rho=6.25 "g/cm"^3`
a=400 pm or `400xx10^(-10)` cm
`therefore V=a^3=(400xx10^(-10))^3`
Z=9
`Z=(rhoxxN_0xxa^3)/M=(6.25xx6.02xx10^23xx(400xx10^(-10))^3)/60`
`therefore` Z=4 Hence, it is face-centred cubic unit cell.
For fcc, `4r=sqrt2a`
`therefore r=(sqrt2a)/4`
`therefore r=(1.414xx400)4`=141.4 pm