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Question

If the kinetic energy of an electron is increased to 16 times the initial value, how many times would the new de Broglie wavelength be?

A
4
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B
0.25
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C
16
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D
0.5
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Solution

The correct option is B 0.25
de Broglie's wavelength in terms of kinetic energy can be given as: λ=h2K.E. m

Let K.Ei and K.Ef be the initial and final kinetic energies while λi,λf are the de Broglie's wavelengths for respective kintetic energies.

It is clear that:
λfλi=K.EiK.Ef

Given that:
K.Ef=16×K.Ei

So,
λfλi=K.Ei16×K.Ei=14λf=14λi

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