The carrier density (number of free electrons per `m^(3)` ) in metallic conductoirs is of the order of

Options

A. `10^(10)`
B. `10^(-16)`
C. `10^(22)`
D. `10^(28)`

Answer

To determine the carrier density (number of free electrons per cubic meter) in metallic conductors, we can follow these steps:

### Step 1: Understand Carrier Density
Carrier density refers to the number of charge carriers (free electrons in the case of metals) per unit volume. In metallic conductors, this value is typically very high due to the presence of a large number of free electrons.

### Step 2: Use the Formula for Current Density
The relationship between current density (J), carrier density (N), charge of an electron (e), and drift velocity (V_d) is given by the formula:
\[ J = N \cdot e \cdot V_d \]
Where:
- \( J \) is the current density (A/m²)
- \( N \) is the carrier density (number of free electrons per m³)
- \( e \) is the charge of an electron (approximately \( 1.6 \times 10^{-19} \) C)
- \( V_d \) is the drift velocity (m/s)

### Step 3: Recognize the Order of Magnitude
In metallic conductors, the carrier density is known to be very high. For most metals, the carrier density is on the order of \( 10^{28} \) electrons per cubic meter. This is a general value that applies to good conductors like copper, silver, and aluminum.

### Step 4: Conclusion
Thus, the carrier density in metallic conductors is approximately:
\[ N \approx 10^{28} \, \text{m}^{-3} \]

### Final Answer
The carrier density in metallic conductors is of the order of \( 10^{28} \, \text{m}^{-3} \).

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