Final answer:
The volume density of Si atoms is 5.00 * 10^22 atoms/cm^3. The areal density of Si atoms on the (100) plane is 1.35 * 10^15 atoms/cm^2. The distance between two adjacent (111) planes in Si is 3.14 * 10^-8 cm.
Step-by-step explanation:
First, let's calculate the volume density of Si atoms. Silicon (Si) has a diamond cubic structure, with a lattice constant of 5.43 Å. Each unit cell of the diamond cubic structure contains 8 atoms at the corners (each corner atom contributed to 8 unit cells), 6 face-centered atoms (each face-centered atom contributed to 2 unit cells), and 4 atoms entirely within the unit cell. Hence, the total number of atoms per unit cell is 8*(1/8) + 6*(1/2) + 4 = 8 atoms. The volume of the unit cell can be calculated using the lattice constant (a), which is the length of the edge of the cubic unit cell:
V = a3 = (5.43 * 10-8 cm)3 = 1.60 * 10-22 cm3
The volume density is then the number of atoms per unit cell divided by the unit cell volume:
Volume Density = 8 atoms / 1.60 * 10-22 cm3 = 5.00 * 1022 atoms/cm3
To find the areal density on the (100) plane, we consider that each atom on the (100) face is shared by four unit cells and that the face itself is a square with side length a:
Areal Density = (1 atom per cell corner * 4 corners) / a2 = 4 / (5.43 * 10-8 cm)2 = 1.35 * 1015 atoms/cm2
Lastly, the distance between two adjacent (111) planes (d111) in Si can be calculated using the lattice constant and the fact that for a cubic crystal, the plane spacing for the (111) plane is given by:
d111 = a / √3 = 5.43 * 10-8 cm / √3 = 3.14 * 10-8 cm