The substance silicon is found to crystallize in a cubic lattice, with an edge length of 541.7 pm. ?

Question

If the density of solid silicon is 2.348 g/cm3, how many Si atoms are there per unit cell?

Answer 1

Volume of unit cell = (541.7 pm)^3 = 1.590X10^8 pm^3

From the density,

2.348 g/cm^3 X (1 cm/10 mm)^3 X (1 mm^3 / 10^9 um^3) X (1 um^3/10^9 nm(^3) X 1 um^3 / 10^9 pm^3) = 2.348X10^-30 g/pm^3

So, (2.348X10^-21 g/pm^3 X 1.590X10^8 pm^3/unit cell / 28.0855 g/mol ) X 6.022X10^23 atoms/mol = 8 atoms/unit cell