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Plot a graph showing variation of de-Broglie wavelength $(\lambda )$ associated with a charged particle mass $m$ , versus $\frac{1}{\sqrt{V}}$ ,

Where $V$ is the potential difference through which the particle is accelerated. How does this graph give us the information regarding the magnitude of the charge of the particle

Answers (1)

Let us consider a particle of charge $q$ and mass $m.$

To gain speed $v$ and kinetic energy $KE,$ Let it be accelerated by a potential difference $V$

Thus,

$KE =qV=\frac{1}{2}mv^2$

Now, on Rearranging the expression, we have

$v=\sqrt{\frac{2qV}{m}}$

The de-Broglie wavelength equation :-

$\lambda =\frac{h}{mv}$

On substituting the value of $v,$ we have

$\lambda=\frac{h}{\sqrt{2mqV}}$

Now, we know the equation of straight line.-

$y=mx,$ Where $m$ is the shape of the line.

Hence, on plotting the graph of $\lambda$ vs $\frac{1}{\sqrt{V}}$ .

We will have a straight line with a slope.

$S=\frac{h}{\sqrt{2mq}}$

On rearranging, we have

$q=\frac{h^{2}}{2mS^{2}}$

The graph of $\lambda$ vs $\frac{1}{\sqrt{V}}$ . Can be drawn as :

Hence, we can determine $S$ from the graph, and this graph gives us the information regarding the magnitude of the charge of the particle.

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Safeer PP

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