First slide

Matter waves (DC Broglie waves)

Question

An electron is accelerated from rest through a potential didifference of V volt. If the de Broglie wavelength of the electron is $1.227 x 10^{- 2}$ nm, the potential difference is :

Easy

A

$10^{2} V$
B

$10^{3} V$
C

$10^{4} V$
D

10 V

Solution

$\begin{array}{l} λ = \frac{h}{mv} \\ = \frac{h}{\sqrt{2 vgm}} \\ \Rightarrow λ = \frac{12 .27}{\sqrt{v}} A^{\circ} \\ 1 .227 \times 10^{- 11} = \frac{12 .27}{\sqrt{v}} \times 10^{- 10} \\ \sqrt{v} = 10^{2} \Rightarrow V = 10^{4} v \end{array}$

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