Q35 / 180 · COMEDK 2022 · Chemistry
How many atoms are present in hcp per unit cell?
- A4
- B2
- C1
- Correct answerD6
Solution
In a hexagonal close packing (hcp) unit cell, the number of atoms is calculated by summing the contributions from atoms at different positions.
The unit cell has 12 atoms at the corners of the hexagonal faces, each contributing $\dfrac{1}{6}$ to the unit cell. Thus, the contribution from corner atoms is $12 \times \dfrac{1}{6} = 2$.
There are 2 atoms at the centers of the top and bottom hexagonal faces, each contributing $\dfrac{1}{2}$ to the unit cell. Thus, the contribution from face-centered atoms is $2 \times \dfrac{1}{2} = 1$.
There are 3 atoms located entirely within the body of the unit cell, each contributing 1 to the unit cell. Thus, the contribution from body-centered atoms is $3 \times 1 = 3$.
The total number of atoms per unit cell is $2 + 1 + 3 = 6$.
Answer: 6
The unit cell has 12 atoms at the corners of the hexagonal faces, each contributing $\dfrac{1}{6}$ to the unit cell. Thus, the contribution from corner atoms is $12 \times \dfrac{1}{6} = 2$.
There are 2 atoms at the centers of the top and bottom hexagonal faces, each contributing $\dfrac{1}{2}$ to the unit cell. Thus, the contribution from face-centered atoms is $2 \times \dfrac{1}{2} = 1$.
There are 3 atoms located entirely within the body of the unit cell, each contributing 1 to the unit cell. Thus, the contribution from body-centered atoms is $3 \times 1 = 3$.
The total number of atoms per unit cell is $2 + 1 + 3 = 6$.
Answer: 6
Hence, the correct answer is option: 'D'.