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An electron of mass m and charge e is accelerated from rest through a potential difference of V volt in vacuum. Its final speed will be

1. √(2eV/m)
2. eV/m
3. 2√(eV/m)
4. eV/√(2m)

Correct answer: √(2eV/m)

Solution

The kinetic energy gained by the electron equals the work done by the electric field, which is eV. Using the relation for kinetic energy, (1/2)mv² = eV, solving for v gives v = √(2eV/m).

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