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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