electron wavelength

Question

Non-relativistic electron of kinetic energy K has de Broglie wavelength proportional to:

RankGuru · Accepted Answer

The relationship between momentum ($p$) and kinetic energy ($K$) is:
$p = \sqrt{2 m K}$
From de Broglie's formula:
$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2 m K}}$
Therefore, $\lambda \propto \frac{1}{\sqrt{K}}$.
If the kinetic energy of the electron increases by a factor of 4, its associated wavelength decreases by half.

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electron wavelength

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