question_answer

The two lines A and B shown in the graph plot the de-Broglie wavelength \[(\lambda )\] as a function of \[1/\sqrt{V}\] (V is the accelerating potential) for two particles having the same charge. Which of the two represents the particle of heavier mass?             

Answer:

                de- Broglie wavelength, \[\lambda =\frac{h}{\sqrt{2mqV}}=\frac{h}{\sqrt{2mq}}.\frac{1}{\sqrt{V}}\]                 \[\therefore \] Slope of \[\lambda \]versus \[1/\sqrt{V}\]graph \[=\frac{h}{\sqrt{2mq}}\]                 For the particle of same charge \[\text{q}\]. Slope \[\propto \frac{1}{\sqrt{m}}\] As the slope of line A is smaller than that of line B, so the line A represents the heavier particle.