Q12 of 47 Page 1

Plot a graph showing variation of de Broglie wavelength (γ) associated with a charged particle of mass m, versus 1/ √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?

Consider a particle of mass , charge . Let it be accelerated through a potential difference to gain speed and Kinetic energy KE.



Now, we can rearrange the expression to get



The de-Broglie wavelength is given by the equation:



Substituting the value of , we get



This analogous to the equation of a straight line passing through the origin: where is the slope of the line.


Hence, we can see that if we plot the graph of vs , we would get a straight line with slope:



On rearranging,



Hence, as we know , and we can determine S from the graph, we can calculate the magnitude of charge on the particle.


The graph is drawn below:



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