In pure semiconductor, the number of conduction electrons is `6 xx 10^18` per cubic meter. 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 find 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: Determine the volume of the sample
The dimensions of the sample are given as:
- Length = 1 cm
- Width = 1 cm
- Height = 1 mm

First, we need to convert these dimensions into meters:
- 1 cm = 0.01 m
- 1 mm = 0.001 m

Now, we can calculate the volume in cubic meters:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = (0.01 \, \text{m}) \times (0.01 \, \text{m}) \times (0.001 \, \text{m}) = 0.0000001 \, \text{m}^3 = 1 \times 10^{-7} \, \text{m}^3 \]

### Step 2: Calculate the number of conduction electrons
The number of conduction electrons per cubic meter is given as:
\[ n = 6 \times 10^{18} \, \text{electrons/m}^3 \]

To find the total number of conduction electrons in the sample, we multiply the number of electrons per cubic meter by the volume of the sample:
\[ \text{Total electrons} = n \times \text{Volume} = (6 \times 10^{18} \, \text{electrons/m}^3) \times (1 \times 10^{-7} \, \text{m}^3) \]
\[ \text{Total electrons} = 6 \times 10^{11} \, \text{electrons} \]

### Step 3: Determine the number of holes
In a pure semiconductor, the number of holes is equal to the number of conduction electrons. Therefore, the number of holes in the sample is also:
\[ \text{Total holes} = 6 \times 10^{11} \, \text{holes} \]

### Final Answer
The number of holes in the sample is \( 6 \times 10^{11} \).

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