Q12.85 P - Chemistry: Molecular Nature Of Matter And Change

Question

What is the number of atoms per unit cell for each metal?

   (a) Polonium, Po              (b) Manganese, Mn (c) Silver, Ag

Step-by-Step Solution

Answer

The number of atoms per unit cell for each given metal is:

 

1. Polonium, Po has one atom per unit cell.
2. Manganese, Mn has two atoms per unit cell.
3. Silver, Ag has four atoms per unit cell.

Step 1: The number of atoms in unit cells.

Considering the contribution of atoms in the unit cell, the atoms in the corner of the cube contribute 1/8^th to one cubic cell, the body-centered atom contributes a whole atom for that cell and the face-centered atom contributes half for the unit cell.

Step 2: Subpart (a) The number of atoms in Polonium (Po).

Polonium, Po has metal atoms in the corner of the cell, thus contributing,

$\mathbf{8}\mathbf{\times }\left(\frac{1}{8}\right)\mathbf{=}\mathbf{1}$

Therefore, a total of one metal atom is present in the cell.

Step 3: Subpart (b) The number of atoms in Manganese (Mn).

Manganese, Mn has metal atoms in the corner as well as in the body center of the cell, thus contributing,

$\mathbf{8}\mathbf{\times }\left(\frac{1}{8}\right)\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{2}$

Therefore, a total of two metal atoms are present in the cell.

Step 4: Subpart (c) The number of atoms in Silver (Ag).

Silver, Ag has metal atoms in the corner as well as in the six-face center of the cell, thus contributing,

$\mathbf{8}\mathbf{\times }\left(\frac{1}{8}\right)\mathbf{+}\mathbf{6}\mathbf{\times }\left(\frac{1}{2}\right)\mathbf{=}\mathbf{4}$

Therefore, a total of four metal atoms are present in the cell.