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

Question

The substance silicon is found to crystallize in a cubic lattice, with an edge length of 541.7 pm. If the density of solid silicon is 2.348 g/cm³, how many Si atoms are there per unit cell?

Answer 1

density of unit cell = z*MW/(V*N)

z = number of atoms

MW = molecular weight = of Si -> 28.066

V = volume (cube in this case, (length of side)³) but you should convert to cm since density uses cm -> 541.7*10^-10 cm

N = Avogadro's number = 6.022*10²³

This problem, you would solve for z

z = density*V*N/MW

= 2.348*(541.7*10^-10)³*6.022*10²³/28.066 = 8 atoms