An electron and a proton starting from rest get accelerated through potential difference of 100 kV. The final speeds of the electron and the proton are Ve and Vp respectively. Which one of the following relations is correct?
- A.Ve > Vp
- B.Ve < Vp
- C.Ve = Vp
- D.Cannot be determined
Correct answer
Explanation
The correct answer is A, Ve > Vp. Both particles gain the same kinetic energy, but the electron is far lighter, so it ends up much faster.
When a charge q is accelerated through a potential difference V, it gains kinetic energy equal to qV. The electron and the proton carry charges of the same size, 1.6 × 10-19 coulomb, so through 100 kV each gains the same energy, 100 keV. Kinetic energy is ½mv², so for equal energy the speed varies inversely as the square root of the mass. A proton is about 1836 times heavier than an electron, so without relativity the electron would move about 43 times faster. At this energy the electron's speed is actually limited by relativity, but it is still well above half the speed of light, while the proton moves at only a few thousand km per second.
Option B is wrong because the heavier proton is the slower one. Option C is wrong because equal energy does not mean equal speed when the masses differ. Option D is wrong because the charges and masses are known, so the speeds can be compared.
Exam tip: same charge, same voltage = same kinetic energy; lighter particle = higher speed.
Practice Questions
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- B.Martin Luther
- C.Johannes Kepler
- D.Copernicus
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- C.Histones are proteins associated with lipids in the cytosol.
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