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)
S safeer

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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