Plot a graph showing variation of de-broglie wavelength λ versus where v is acclerating potential for two particles A and B carrying same charge but of masses m1, m2(m1 > m2). Which one of the two represents a particle of smaller mass and why?

Engineering

Physics

Calculus

Photoelectric Effect Einsteins Equation

de Broglie Hypothesis and Dual Nature

Question

Plot a graph showing variation of de-broglie wavelength λ versus $\frac{1}{\sqrt{V}}$ where v is acclerating potential for two particles A and B carrying same charge but of masses m₁, m₂(m₁ > m₂). Which one of the two represents a particle of smaller mass and why?

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The de-Broglie wavelength is given by

$λ = \frac{h}{\sqrt{2 mqV}}$

The graph of $λ$ vs $\frac{1}{\sqrt{V}}$ is a straight line with slope $\frac{h}{\sqrt{2 mq}}$

Since charge q of A and B is same , slope is $\frac{1}{\sqrt{m}}$

Since, m₁ > m₂

Slope of B < Slop of A

More is the slope, less is the mass, since slope of A is larger .So plot A represents smaller mass m₂