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?
- A.The kinetic energy of both the particles will be different.
- B.The speed of the electron will be higher than that of the proton.
- C.The speed of the proton will be higher than that of the electron.
- D.The speed of the electron and the proton will be equal.
Correct answer
Explanation
The correct answer is B, The speed of the electron will be higher than that of the proton. Both gain the same kinetic energy, but the electron is far lighter, so it moves much faster.
A charge q accelerated through a potential difference V gains kinetic energy qV. The electron and the proton carry charges of the same size, e, so each gains 1000 eV, or about 1.6 × 10⁻¹⁶ J. Since kinetic energy is ½mv², the speed is √(2qV/m). The proton is about 1836 times as heavy as the electron, so the electron's speed is about √1836, roughly 43 times, the proton's. (The electron is pushed one way and the proton the other, but the energy gained is the same.)
Option A is wrong because equal charge and equal voltage give equal kinetic energy. Option C is wrong because the heavier proton is the slower one. Option D is wrong because equal energy with unequal masses cannot give equal speeds.
Exam tip: same charge and same voltage give the same energy, qV; the lighter particle is the faster one.
Practice Questions
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- B.Martin Luther
- C.Johannes Kepler
- D.Copernicus
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- D.Eyepiece-Objective lens-Body tube-Mirror
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- B.Histones are proteins that are present in nucleus in association with DNA.
- C.Histones are proteins associated with lipids in the cytosol.
- D.Histones are proteins associated with carbohydrates in the cytosol.
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