2. (a) The radius of a silicon atom can be expressed as half of the distance between the
closest (touching) atoms, which are on the main diagonal of the lattice cube.
(b) The numbers of Si atom in its diamond structure are 8.
So the density of silicon atoms is
(c) The density of Si is
4. (a) The molecular weight of boron is 10.81.
The boron concentration can be given as
(b) The average occupied volume of everyone boron atoms in the wafer is
V= 1/nb = 1/9.78*1018 cm3
If we assume that the volume is a sphere with diameter d then
d = 2 (3V/4π)1/3 = 5.8*10-7 cm
An alternative method considers the volume as a cube with the distance between atoms
equal to the cube edge, which gives
d = (V)1/3 = 4.7*10-7 cm