The de Broglie wavelength of an electron having kinetic energy E is λ . If the kinetic energy of electron becomes E 4 , then its de-Broglie wavelength will be:

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The de-Broglie wavelength in the first case is
$λ = \frac{h}{\sqrt{2 m E}}$
In the second case the kinetic energy is $K = \frac{E}{4}$ .
Let the de-Broglie wavelength be $λ'$ .
The value of wavelength is
$λ' = \frac{h}{\sqrt{2 m \frac{E}{4}}} = \frac{2 h}{\sqrt{2 m E}} = 2 λ$

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