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The De Broglie Explanation

If the kineti...

Question

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is

A

25

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B

75

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C

60

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D

50

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Solution

The correct option is B 75
$λ = \frac{h}{p} = \frac{h}{\sqrt{2 m E}} (∵ p = \sqrt{2 m E}) λ^{'} = \frac{h}{\sqrt{2 m (16 E)}} = \frac{λ}{4} = 0.25 λ$
% change=-75% ie. De-Broglie wave length will decrease by 75%

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