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An electron and a proton starting from rest are accelerated through a

June 1, 2025 by rawan239

An electron and a proton starting from rest are accelerated through a potential difference of 1000 V. Which one of the following statements in this regard is correct?

The kinetic energy of both the particles will be different.

The speed of the electron will be higher than that of the proton.

The speed of the proton will be higher than that of the electron.

The speed of the electron and the proton will be equal.

This question was previously asked in

UPSC CDS-2 – 2017

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The speed of the electron will be higher than that of the proton.

When an electron and a proton, both starting from rest, are accelerated through the same potential difference V, they gain the same kinetic energy (KE). The kinetic energy gained is equal to the work done by the electric field, which is qV, where q is the charge of the particle and V is the potential difference. The magnitude of charge is the same for both electron and proton (|q_e| = |q_p|). So, KE_electron = KE_proton = |q|V.

Kinetic energy is given by KE = 1/2 * mv², where m is the mass and v is the speed. Since KE is the same for both particles, and the mass of the electron (m_e) is significantly less than the mass of the proton (m_p) (m_e ≈ m_p/1836), for the equation 1/2 * m_e * v_e² = 1/2 * m_p * v_p² to hold, the velocity of the lighter particle (electron) must be greater than the velocity of the heavier particle (proton). Thus, v_e > v_p.

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