JEE Main 2024

Question

According to the wave particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron ($\lambda$) and momentum of electron (p)?

![Options](https://www.edvaya.com/jee/chemistry/q32-options-graphs-2024.png) A). Graph representing a hyperbola plotting $\lambda$ vs $p$ B). Graph representing a straight line plotting $p$ vs $\lambda$ C). Graph representing a hyperbola plotting $\lambda$ vs $1/p$ D). Graph representing a straight line plotting $\lambda$ vs $p$

Edvaya · Accepted Answer

The correct answer is Graph representing a hyperbola plotting $\lambda$ vs $p$. **Solution:** According to the de Broglie equation: $\lambda = \frac{h}{p}$ This means $\lambda \propto \frac{1}{p}$. The relationship between $\lambda$ and $p$ is inversely proportional. A plot of variables that are inversely proportional yields a rectangular hyperbola. Thus, the graph of $\lambda$ versus $p$ will be a hyperbolic curve in the first quadrant.

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