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The mean free path of electrons in a metal is 4 × 10⁻⁸ m. The electric field which can give an average 2 eV energy to an electron in the metal will be in units of V/m

1. 5 × 10¹¹
2. 8 × 10¹¹
3. 5 × 10⁷
4. 8 × 10⁷

Correct answer: 5 × 10⁷

Solution

The energy gained by an electron in an electric field is given by eEλ, where e is the charge of the electron, E is the electric field, and λ is the mean free path. Setting this equal to 2 eV and solving for E, we get E = (2 × 1.6 × 10⁻¹⁹) / (4 × 10⁻⁸) = 8 × 10⁷ V/m.

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