To calculate the density of silicon, we need to know its atomic mass. The atomic mass of silicon is 28.0855 g/mol.
We also know that the interatomic spacing of silicon is 0.235 nm.
Using this information, we can calculate the volume of an individual silicon atom:
Volume of a sphere with radius 0.235/2 = 0.1175 nm = (4/3)π(0.1175)^3 = 6.06 x 10^-4 nm^3
There are Avogadro's number of silicon atoms in 1 mole of silicon, which is 6.022 x 10^23.
So the volume of 1 mole of silicon = (6.022 x 10^23 atoms/mole) x (6.06 x 10^-4 nm^3/atom) = 3.65 x 10^-10 m^3/mole
The mass of 1 mole of silicon is its atomic mass in grams, which is 28.0855 g/mole.
Now we can calculate the density of silicon:
Density = mass/volume = 28.0855 g/mole / 3.65 x 10^-10 m^3/mole = 2.33 x 10^3 kg/m^3
Therefore, the density of silicon is 2.33 x 10^3 kg/m^3.