First slide

Wave nature of matter

Question

An electron is accelerated through a potential difference of V volt. It has a wavelength $λ$ associated with it. Through what potential difference an electron must be accelerated so that its de Broglie wavelength is the same as that of a proton? Take mass of proton to be 1837 times larger than the mass of electron.

Easy

A

V volt
B

1837V volt
C

V/1837 volt
D

$\sqrt{1837} V volt$

Solution

$\begin{array}{l} λ = \frac{h}{\sqrt{2 m q V}} \\ \Rightarrow m V = constant \\ \Rightarrow 1837 V' = 1 \times V \\ \Rightarrow V^{'} = \frac{V}{1837} volt \end{array}$

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