In pure semiconductor, the number of conduction electrons is `6 xx 10^18` per cubic metre. How many holes are there in a sample of size 1 cm x 1 cm x 1 mm?

Options

A. `3xx10^10`
B. `6xx10^11`
C. `3xx10^11`
D. `6xx10^10`

Explanation

To solve the problem of finding the number of holes in a pure semiconductor sample of size 1 cm x 1 cm x 1 mm, we can follow these steps:

### Step 1: Understand the relationship between conduction electrons and holes
In a pure semiconductor, the number of conduction electrons is equal to the number of holes. Therefore, if we know the number of conduction electrons, we can directly say that the number of holes is the same.

### Step 2: Calculate the volume of the sample
The dimensions of the sample are given as:
- Length = 1 cm = 0.01 m
- Width = 1 cm = 0.01 m
- Height = 1 mm = 0.001 m

To find the volume (V) of the sample, we use the formula for the volume of a rectangular prism:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ V = 0.01 \, \text{m} \times 0.01 \, \text{m} \times 0.001 \, \text{m} = 1 \times 10^{-6} \, \text{m}^3 \]

### Step 3: Calculate the number of conduction electrons in the sample
We are given that the number of conduction electrons is \(6 \times 10^{18}\) per cubic meter. To find the total number of conduction electrons (N) in the sample, we multiply the number of conduction electrons per cubic meter by the volume of the sample:
\[ N = \text{Number of conduction electrons per m}^3 \times V \]
Substituting the values:
\[ N = 6 \times 10^{18} \, \text{m}^{-3} \times 1 \times 10^{-6} \, \text{m}^3 \]
\[ N = 6 \times 10^{12} \]

### Step 4: Determine the number of holes
Since the number of holes is equal to the number of conduction electrons in a pure semiconductor, we conclude that:
\[ \text{Number of holes} = N = 6 \times 10^{12} \]

### Final Answer
The number of holes in the sample is \(6 \times 10^{12}\).

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