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NEET 2013

Exam: NEET
Year: 2013
Subject: Physics
Chapter: Dual Nature of Matter

NEET 2013 · Physics · Dual Nature of Matter

The wavelength λ_e of an electron and λ_p of a photon of same...

The wavelength

\lambda_e

of an electron and

\lambda_p

of a photon of same energy

E

are related by

Options

A $\lambda_p \propto \lambda_e^2$
B $\lambda_p \propto \lambda_e$
C $\lambda_p \propto \sqrt{\lambda_e}$
D $\lambda_\rho \propto \frac{1}{\sqrt{\lambda_e}}$

Correct answer

A. $\lambda_p \propto \lambda_e^2$

Step-by-step solution

Wavelength of electron,

\begin{aligned}& \lambda_e=\frac{h}{\sqrt{2 m E}}\\ & \text{ and proton } \lambda_p=\frac{h c}{E}\\ & \Rightarrow \quad \lambda_e^2=\frac{h^2}{2 m E} \text{ or }E=\frac{h c}{\lambda_p}\\ & \therefore \quad \lambda_e^2=\frac{h^2}{2 m \cdot \frac{h c}{\lambda_p}} \Rightarrow \lambda_e^2=\frac{h^2}{2 m h C} \lambda_p \\ & \Rightarrow \quad \lambda_e^2 \propto \lambda_p \end{aligned}

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