CBSE Class 12 · 2009 · Modern PhysicsShort Answer

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An electron and a proton are accelerated through the same potential. Which one of the two has
(i) the greater value of de-Broglie wavelength associated with it, and
(ii) less momentum? Justify your answer.

Answer: Electron has the greater $λ$ and the smaller momentum.

Solution

For a charge accelerated through potential

V

λ = \frac{h}{2 m q V}

, so

λ \propto \frac{1}{m}

(same

q

V

).
(i) The electron, being much lighter, has the greater de-Broglie wavelength.
(ii) Momentum

p = \frac{h}{λ}

, so a larger wavelength means smaller momentum; hence the electron has less momentum.

Electron: larger λ and smaller p

CBSE Class 12 Board · 2009 · Subjective

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