If the resistivity of copper is `1.7 xx 10^(-6) Omega cm`, then the mobility of electrons in copper, if each atom of copper contributes one free electron for conduction, is [The amomic weight of copper is `63.54` and its density is `8.96 g//c c]` :

Options

A. `23.36 cm^(2)//Vs`
B. `503.03cm^(2)//Vs`
C. `43.25 cm^(2)//Vs`
D. `88.0 cm^(2)//Vs`

Explanation

To find the mobility of electrons in copper, we will follow these steps:

### Step 1: Understand the relationship between resistivity, conductivity, and mobility
The mobility (μ) of electrons can be calculated using the formula:
\[ \mu = \frac{\sigma}{n \cdot e} \]
where:
- \(\sigma\) is the conductivity,
- \(n\) is the number of free electrons per unit volume,
- \(e\) is the charge of an electron (\(1.6 \times 10^{-19} \, \text{C}\)).

### Step 2: Calculate conductivity from resistivity
Given the resistivity (\(\rho\)) of copper is \(1.7 \times 10^{-6} \, \Omega \cdot \text{cm}\), the conductivity (\(\sigma\)) is given by:
\[ \sigma = \frac{1}{\rho} = \frac{1}{1.7 \times 10^{-6}} \, \text{S/cm} \]

### Step 3: Calculate the number of free electrons per unit volume (n)
To find \(n\), we use the density and atomic weight of copper:
- Density of copper (\(d\)) = \(8.96 \, \text{g/cm}^3\)
- Atomic weight of copper (\(M\)) = \(63.54 \, \text{g/mol}\)

The number of atoms per unit volume can be calculated using:
\[ n = \frac{d \cdot N_A}{M} \]
where \(N_A\) (Avogadro's number) = \(6.022 \times 10^{23} \, \text{atoms/mol}\).

Substituting the values:
\[ n = \frac{8.96 \, \text{g/cm}^3 \cdot 6.022 \times 10^{23} \, \text{atoms/mol}}{63.54 \, \text{g/mol}} \]

### Step 4: Calculate the mobility (μ)
Now we can substitute \(\sigma\), \(n\), and \(e\) into the mobility formula:
\[ \mu = \frac{\sigma}{n \cdot e} \]

### Step 5: Substitute the calculated values and solve
1. Calculate \(\sigma\):
\[ \sigma = \frac{1}{1.7 \times 10^{-6}} \approx 588.24 \, \text{S/cm} \]

2. Calculate \(n\):
\[ n = \frac{8.96 \cdot 6.022 \times 10^{23}}{63.54} \approx 8.5 \times 10^{22} \, \text{electrons/cm}^3 \]

3. Substitute into the mobility formula:
\[ \mu = \frac{588.24}{(8.5 \times 10^{22}) \cdot (1.6 \times 10^{-19})} \]

4. Calculate \(\mu\):
\[ \mu \approx \frac{588.24}{1.36 \times 10^{4}} \approx 43.25 \, \text{cm}^2/\text{V}\cdot\text{s} \]

### Final Answer:
The mobility of electrons in copper is approximately \(43.25 \, \text{cm}^2/\text{V}\cdot\text{s}\).

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