If the lattice constant of silicon is 5.43 Å, calculate?
(a) the distance from the center of one silicon atom to the center of its nearest neighbor,
(b) the number density of silicon atoms (#/cm 3 ), and
(c) the mass density (g/cm 3 ) of silicon.

(a). The distance from the center of one silicon atom to the center of its nearest neighbor is

(b). The number density of silicon atoms is .

(c). The mass density is

Explanation:

Given that,

Lattice constant of silicon

We know that,

The nearest atom distance is

The radius of each atom is

Put the value into the formula

The center of the one silicon atom to the center of its nearest neighbor is equal to the twice the radius of the atom

(a). We need to calculate the nearest neighbor distance

Using formula of distance

(b). We need to calculate the number density of silicon atoms

Using formula for the number density of silicon atoms

(c). We need to calculate the number of atoms

Using formula for number of atoms

Put the value into the formula

We need to calculate the mass density

Using formula of mass density

Put the value into the formula

Hence, (a). The distance from the center of one silicon atom to the center of its nearest neighbor is

(b). The number density of silicon atoms is .

(c). The mass density is

15.3 cos 65 degrees trig