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De Broglie's Hypothesis

If an electro...

Question

If an electron having kinetic energy $2 e V$ is accelerated through the potential difference of $2 V o l t$ , then calculate the de-Broglie wavelength associated with the electron.

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Solution

De broglie wavelength is given by,
According to de broglie hypothesis $λ$ = $\frac{h}{p} = \frac{h}{(2 m e V)^{\frac{1}{2}}}$
By substituting $e = 1.6 \times 10^{- 19} C$ , $m = 9.108 \times 10^{- 25} k g$ and
$h = 6.63 \times 10^{- 34} J s$
Therefore,
$λ$ $= \frac{12.27}{(2)^{\frac{1}{2}}}$
$λ$ = $8.52 A^{0}$

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