In the crystalline solids the smallest repeating part in the lattice is known as unit cell. The unit cells are described as simple (points at all corners), body centred (points at all the corners and it the centre), face centred (points at all the corners and centre of all faces), and end centred (points at all hte corners and centres of two opposite and faces) unit cells. In two common tyupes of packing ccp and hcp, 26% of space is left unoccupied in the form of interstitial sites. For the stable ionic crystalline structures, there is difinite radius ratio limit for a cation to fit perfectly in the lattice of anions, called radius ratio rule. This also defines the coordination number of an ion, which is the number of nearest neighbours of opposite charges. This depeds upon the ratio of radii of two types of ions, `r_(+)//r_(-)`. This ratio for coordination numbers 3,4,6,and 8 is respectively 0.155 - 0.225, 0.225 - 0.414, 0.414 - 0.732 and 0.732 - 1 respectively.
The number of atoms per unit cell in simple (s), body centred(b) , face centred (f) and end centred (e) unit cell decreases as

Options

A. f > b > e > s
B. f > b = e > s
C. b > f > s = e
D. f > b > e = s

Explanation

To solve the question regarding the number of atoms per unit cell in different types of unit cells (simple, body-centered, face-centered, and end-centered), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Simple Unit Cell (s)**:
- A simple unit cell has atoms located only at the corners.
- There are 8 corners in a cube, and each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total number of atoms per unit cell in a simple unit cell is:
\[ \text{Number of atoms} = 8 \times \frac{1}{8} = 1 \]

2. **Understanding Body-Centered Unit Cell (b)**:
- A body-centered unit cell has atoms at all corners and one atom at the center of the cube.
- Again, there are 8 corner atoms contributing \( \frac{1}{8} \) each, plus 1 atom at the center contributing fully.
- Therefore, the total number of atoms per unit cell in a body-centered unit cell is:
\[ \text{Number of atoms} = 8 \times \frac{1}{8} + 1 = 2 \]

3. **Understanding Face-Centered Unit Cell (f)**:
- A face-centered unit cell has atoms at all corners and at the center of each face.
- There are 8 corner atoms contributing \( \frac{1}{8} \) each, and there are 6 faces with each face contributing \( \frac{1}{2} \) of an atom.
- Therefore, the total number of atoms per unit cell in a face-centered unit cell is:
\[ \text{Number of atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

4. **Understanding End-Centered Unit Cell (e)**:
- An end-centered unit cell has atoms at all corners and at the center of two opposite faces.
- There are 8 corner atoms contributing \( \frac{1}{8} \) each, and there are 2 faces contributing \( \frac{1}{2} \) each.
- Therefore, the total number of atoms per unit cell in an end-centered unit cell is:
\[ \text{Number of atoms} = 8 \times \frac{1}{8} + 2 \times \frac{1}{2} = 1 + 1 = 2 \]

5. **Arranging the Number of Atoms in Decreasing Order**:
- Now, we have the following number of atoms per unit cell:
- Simple (s): 1 atom
- Body-centered (b): 2 atoms
- Face-centered (f): 4 atoms
- End-centered (e): 2 atoms
- Arranging these in decreasing order gives:
- Face-centered (f) > Body-centered (b) = End-centered (e) > Simple (s)

### Final Answer:
- The order of the number of atoms per unit cell from highest to lowest is:
\[ f > b = e > s \]