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

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

Short Answer

Expert verified

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 by step solution

01

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 1/8th 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.

02

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

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

8×(18)=1

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

03

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,

8×(18)+1=2

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

04

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,

8×(18)+6×(12)=4

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

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