Question

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:
(A) ${10^2}V$
(B) ${10^3}V$
(C) ${10^4}V$
(D) $10V$

Answer 1

In order to answer this question, first we will rewrite the given de Broglie wavelength and then we will apply the formula of de-Broglie wavelength in terms of potential difference, i.e.. $\therefore \lambda = \dfrac{{1.227}}{{\sqrt V }}nm$ , to find the potential difference of an electron.

Complete step by step solution:
Given that-
The potential difference of an electron is, $V\,volt$ .
The de Broglie wavelength of the electron is, $\lambda = 1.227 \times {10^{ - 2}}nm$
To find the potential difference, we will apply the formula of de-Broglie wavelength in terms of potential difference:-
$\therefore \lambda = \dfrac{{1.227}}{{\sqrt V }}nm$
where, $\lambda$ is the wavelength of an electron,
$V$ is the potential difference of an accelerated electron.
$\Rightarrow V = {(\dfrac{{1.227}}{\lambda })^2}$
Now, we will put the value of wavelength of an electron in the above equation:
$\Rightarrow V = {(\dfrac{{1.227}}{{1.227 \times {{10}^{ - 2}}}})^2} \\\ \Rightarrow V = {10^4}volt \\\$
Therefore, the required potential difference is ${10^4}V$ .
Hence, the correct option is (C) ${10^4}V$ .

Note:
There is another situation in which we can find the potential difference, if the current and resistance is given by the circuit or we can find the potential difference between two points by applying the formula, $V = IR$ , where $I$ is the current and $R$ is the resistance.