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Radiation and Dual Nature of Matter — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsRadiation and Dual Nature of Matter4 Marks
Question
Plot a graph showing variation of de-Broglie wavelength $ \lambda $ versus $ 1/\sqrt{V} $ where V is accelerating potential for two particles A and B carrying same charge but of masses $ m_{1} $ and $ m_{2} $, where $ m_{1}>m_{2} $
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Answer

de-Broglie wavelength :
$ \lambda=\frac{h}{\sqrt{2m(qV)}} $
$\Rightarrow \quad \frac{1}{\sqrt{V}}=\left[\frac{\sqrt{2 m q}}{h}\right] \times \lambda$
$\Rightarrow \quad 1 / \sqrt{ V } \propto \lambda$
( $\because q$ is the same for both the particles and 2 and $h$ are constants hence $\sqrt{2 m q} / h$ is a constant.)
Hence the plot of $ 1/\sqrt{V} $ versus de-Broglie wavelength $\lambda$ will be a straight line whose slope is $ \sqrt{2mq}/h $. i.e. it is directly proportional to $\sqrt{m}$. Now since $ m_{1} $ of A is greater than $ m_{2} $ for B.
Image
Hence slope of $ (1/\sqrt{V}-\lambda) $ graph for A will be greater than for B. Hence the graphs for these particles will be as shown in adjacent figure.
But In the figure slope of line A is greater than for line B. Therefore $ m_{1}>m_{2} $. Thus line A represent the particle of large mass.

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