Potential difference of 100 V is applied to the ends of a copper wire one metre long. Calculate the average drift velocity of the electrons ? Compare it with thermal velocity at `27^@C`. Consider there is one conduction electron per atom. The density of copper is `9.0xx10^(3)kg//m^(3)`, Atomic mass of copper is 63.5 g. Avogadro's number `= 6.0 xx 10^(23)` per gram-mole. Conductivity of copper is `5.81 xx 10^(7)Omega^(-1)m^(-1)`. Boltzmann constant `= 1.38 xx10^(23)JK^(-1)`.

Explanation

To solve the problem step by step, we will calculate the average drift velocity of the electrons in the copper wire and then compare it with the thermal velocity at 27°C.

### Step 1: Calculate the number density of conduction electrons (n)
Given:
- Density of copper (ρ) = \(9.0 \times 10^3 \, \text{kg/m}^3\)
- Atomic mass of copper (M) = 63.5 g = \(63.5 \times 10^{-3} \, \text{kg}\)
- Avogadro's number (N_A) = \(6.0 \times 10^{23} \, \text{atoms/mol}\)

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