The total number of current careers in intrinsic semiconductor of dimensions `1m×1m×10^(-2)m` having number of free electrons `n_e=5×10^8 `per cubic metre is

Options

A. `10^18`
B. `10^17`
C. `10^16`
D. `10^15`

Answer

To find the total number of current carriers in the intrinsic semiconductor, we can follow these steps:

### Step 1: Calculate the Volume of the Semiconductor
The dimensions of the semiconductor are given as \(1 \, \text{m} \times 1 \, \text{m} \times 10^{-2} \, \text{m}\).

The volume \(V\) can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the values:
\[ V = 1 \, \text{m} \times 1 \, \text{m} \times 10^{-2} \, \text{m} = 10^{-2} \, \text{m}^3 \]

### Step 2: Identify the Number of Free Electrons per Cubic Meter
The number of free electrons \(n_e\) is given as:
\[ n_e = 5 \times 10^8 \, \text{per cubic meter} \]

### Step 3: Calculate the Total Number of Current Carriers
To find the total number of current carriers (which are the free electrons in this case), we multiply the number of free electrons per cubic meter by the volume of the semiconductor:
\[ \text{Total Current Carriers} = n_e \times V \]
Substituting the known values:
\[ \text{Total Current Carriers} = (5 \times 10^8 \, \text{m}^{-3}) \times (10^{-2} \, \text{m}^3) \]
Calculating this gives:
\[ \text{Total Current Carriers} = 5 \times 10^8 \times 10^{-2} = 5 \times 10^{6} \]

### Final Answer
The total number of current carriers in the intrinsic semiconductor is:
\[ 5 \times 10^{6} \]

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