Aluminum, Al$,$ crystallizes in a face centered cubic unit cell. The density of the metal is $2\mathrm{.}7$ g$/$cm $3.$ A scientist believes that the radius of one Al atom is $1\mathrm{.}69$ x $10^8$ cm$.$ He uses this number to calculate Avogadro's number. What number does he get? $($Hint: It is not $(6\mathrm{.}022$ x $10^23).1)$Think about the relationship between radius and length in a FCC unit cell. What is the length of cell? $2)$With the length of cube in hand, we could calculate the volume of the unit cell by cubing it$.3)$We know the volume of a unit cell, the density of the cell is given by the question. We will use those information to calculate the mass of a unit cell. $4)$How many atoms are in a FCC structured unit cell? There are $4!$ What is the mass of each atom?