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. `10^7`
C. `10^16`
D. `10^15`

Answer

To find the total number of current carriers in an intrinsic semiconductor with given dimensions and free electron concentration, we can follow these steps:

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

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} = 1 \, \text{m} \times 1 \, \text{m} \times 10^{-2} \, \text{m} = 10^{-2} \, \text{m}^3 \]

### Step 2: Determine the Number of Free Electrons
The number of free electrons per cubic meter is given as \(n_e = 5 \times 10^8 \, \text{m}^{-3}\).

To find the total number of free electrons in the semiconductor, we multiply the number of free electrons per cubic meter by the total volume of the semiconductor.

\[ \text{Total free electrons} = n_e \times \text{Volume} = (5 \times 10^8 \, \text{m}^{-3}) \times (10^{-2} \, \text{m}^3) \]

Calculating this gives:

\[ \text{Total free electrons} = 5 \times 10^8 \times 10^{-2} = 5 \times 10^6 \]

### Step 3: Calculate the Total Number of Current Carriers
In an intrinsic semiconductor, the number of holes is equal to the number of free electrons. Therefore, the total number of current carriers (which includes both free electrons and holes) is given by:

\[ \text{Total current carriers} = \text{Total free electrons} + \text{Total holes} \]

Since the number of holes is equal to the number of free electrons:

\[ \text{Total current carriers} = 5 \times 10^6 + 5 \times 10^6 = 10 \times 10^6 = 10^7 \]

### Final Answer
Thus, the total number of current carriers in the intrinsic semiconductor is \(10^7\).

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