Two lines A and B shown in the graph represent the de Broglie wav… - Vidyadip

Question

Two lines A and B shown in the graph represent the de Broglie wavelength $(\lambda)$ as a function of $\frac{1}{\sqrt{\text{V}}}$ (V is the accelerating potential) for two particles having the same charge. Which of the two represents the particle of smaller mass?

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Answer

de Broglie wavelength $\lambda=\frac{\text{h}}{\sqrt{2\text{mqV}}}$ or $\lambda=\frac{\text{h}}{\sqrt{2\text{mq}}}.\frac{1}{\sqrt{\text{V}}}$
The graph of $\lambda$ versus $\frac{1}{\sqrt{\text{V}}}$ is a straight line of slope $\frac{\text{h}}{\sqrt{2\text{mq}}}\propto\frac{1}{\sqrt{\text{m}}}.$ The slope of line B is large, so particle B has smaller mass.

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