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The number of terrahedral and octahedral...

The number of terrahedral and octahedral holes in a hexagonal primitive unit cell are respectively:
(a)8,4
(b)6,12
(c)2,1
(d)12,6

A

8,4

B

6,12

C

2,1

D

12,6

Text Solution

AI Generated Solution

The correct Answer is:
To determine the number of tetrahedral and octahedral holes in a hexagonal primitive unit cell, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the number of atoms in the hexagonal primitive unit cell**: - A hexagonal close-packed (HCP) structure has 6 atoms per unit cell. 2. **Calculate the number of octahedral voids**: - The number of octahedral voids in a crystal structure is equal to the number of atoms present in the unit cell. - Therefore, for a hexagonal primitive unit cell: \[ \text{Number of octahedral voids} = n = 6 \] 3. **Calculate the number of tetrahedral voids**: - The number of tetrahedral voids is given by the formula: \[ \text{Number of tetrahedral voids} = 2 \times n \] - Substituting the value of \( n \): \[ \text{Number of tetrahedral voids} = 2 \times 6 = 12 \] 4. **Summarize the results**: - The number of tetrahedral holes is 12. - The number of octahedral holes is 6. 5. **Select the correct option**: - Based on the calculations, the correct option that matches the number of tetrahedral and octahedral holes is (d) 12, 6. ### Final Answer: The number of tetrahedral and octahedral holes in a hexagonal primitive unit cell are respectively: **12 and 6**. Thus, the answer is (d) 12, 6. ---
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