An electron is accelerated from rest through a potential difference of volt. If the de Broglie wavelength of the electron is nm, the potential difference is [2020]

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Solution

Q.
An electron is accelerated from rest through a potential difference of $V$ volt. If the de Broglie wavelength of the electron is $1.227 \times 10^{- 2}$ nm, the potential difference is [2020]

1 10 V

2 $10^{2}$ V

3 $10^{3}$ V

4 $10^{4}$ V

Ans.
(4)

Given : de-Broglie wavelength of electron

$λ = 1.227 \times 10^{- 2}$ $nm = 0.1227$ $Å$

$∵$ $λ = \frac{h}{\sqrt{2 m e V}} = \frac{12.27}{\sqrt{V}}$ $Å$

We have, $\sqrt{V} = \frac{12.27}{0.1227} = 100 \Rightarrow V = 10^{4}$ $V .$

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