An element X crystallises in fcc structure. 208 g of it has `4.2832 xx 10^(24)` atoms. Calculate the edge of the unit cell, if density of X is `7.2 g cm^(-3)`

Explanation

For fcc structure, `Z=4, d= 7.2 g//cm^3`
Let a be the edge length in pm
We know that density, `d=(ZxxM)/(a^3 xx10^(-30))`
Mass per atom, `M=(208)/(4.2832xx10^(24)`
`a^3 =(ZxxM)/(d xx 10^(-30)) = (4 xx 208)/(7.2xx4.2832 xx 10^(24) xx10^(-30))`
`= 26.97 xx10^6 "pm"^3 implies a = (27 xx10^6)^(1/3) = 300` pm