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NEET PHYSICSEasy

The mean free path of electrons in a metal is 4 × 10⁻⁸ m. The electric field which can give on an average 2 eV energy to an electron in the metal will be in a unit of V m⁻¹:

A

8 × 10⁷

B

5 × 10⁻¹¹

C

8 × 10⁻¹¹

D

5 × 10⁷

Step-by-Step Solution

The energy (WW) gained by an electron accelerating through a distance (dd) under the influence of an electric field (EE) is given by the work done: W=Fd=(eE)dW = Fd = (eE)d. Given: Energy (WW) = 2 eV Distance (dd, mean free path) = 4×1084 \times 10^{-8} m

Substituting the values (noting that 2 eV energy corresponds to the work done on charge ee moving through a potential difference of 2 Volts, or simply equating eVeV units): eEd=2 eVeEd = 2 \text{ eV} E×d=2 VE \times d = 2 \text{ V} E=2 V4×108 mE = \frac{2 \text{ V}}{4 \times 10^{-8} \text{ m}} E=0.5×108 V/mE = 0.5 \times 10^8 \text{ V/m} E=5×107 V/mE = 5 \times 10^7 \text{ V/m}

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