Question

Calculate the theoretical density of silicon of given that the Si-Si bond distance is 0.235 nm. Give your results in megagrams per metter cubed (Mg/m^3).

Answer 1

Si-Si bond distance

d = 0.235 nm

nearest neighbor to atom = 0.25 of body diagonal

body diagonal of cube = ?3 a

d = ?3 a/4

0.235 = ?3 a/4

a = 0.235*4/?3

= 0.543 nm

Volume = 0.543^3 = 0.160103007 nm3 x (1m/10^9nm)³

= 1.601 x 10^-28 m3

Number of atoms in cubic unit cell

Nu = 8×1/8 + 6 ×1/2 + 4

= 8

Molar mass of Si = 28.085 amu

1amu = 1.660 ×10^?27 kg

Total mass = 8 x 28.085 x 1.660 ×10^?27 kg

= 3.729 x 10^-25 kg

Density = mass/volume

= 3.729 x 10^-25 kg / 1.601 x 10^-28 m3

= 2329.1255 kg/m3 x 0.001 Mg/kg

= 2.329 Mg/m3