Question

An electron is accelerated through voltage. Its frequency will be ($e$= charge on electron, $h$= Planck's constant).
A) $eV$
B) $eVh$
C) $\dfrac{{eV}}{h}$
D) $\dfrac{h}{{eV}}$

Answer 1

Hint:In order to find the value of the frequency at which an electron is accelerated, we should use the planck's equation of the energy gained by an electron and compare this value with the other equation for energy gained by an electron which is in terms of the charge of the electron and the voltage through which the electron is accelerated.

Complete step by step answer: Let’s define all the data given in the question.
$e$= charge on electron
$h$= Planck's constant

It is given that the electron is accelerated through a voltage. Let’s take this voltage as $V$.
We know when an electron is accelerated, it will gain an energy within and it is given by the charge multiplied with the voltage through which it is accelerated.
That is, the energy gained by the electron, $E = eV$ …………………………………………………… (1)
Also, from Planck’s law, we know, energy gained is given by the frequency multiplied by the Planck’s constant.
That is, the energy gained by the electron, $E = \nu

h$…………………………………………………… (2)

Where, $h$= Planck's constant

$\nu $=The frequency

Comparing both the equations (1) and (2), we get,
That is, the energy gained by the electron, $E = eV = \nu h$
From this equation, we get the value of frequency, and is given by,
The frequency, $\nu = \dfrac{{eV}}{h}$

The final answer is option (C) $\nu = \dfrac{{eV}}{h}$

Note:The Planck's constant or Planck constant, is the quantum of electromagnetic action that relates a photon's energy to its frequency. The Planck constant multiplied by an electron's frequency is equal to its energy.
The Planck constant is defined to have the exact value \[h = {\text{ }}6.62607015 \times {10^{ - 34}}{\text{ }}J \cdot s\]in SI units.