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Dual Nature of Radiation and Matter question

2024 · Q157
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Dual Nature of Radiation and Matter question

2024 · Q157

NEETPhysicsDual Nature of Radiation and MatterMCQ+4 / −1

An electron and an alpha particle are accelerated by the same potential difference. Let λe\lambda_eλe​ and λα\lambda_\alphaλα​ denote the de-Broglie wavelengths of the electron and the alpha particle, respectively, then:

  1. A
    λe>λα\lambda_e>\lambda_\alphaλe​>λα​
  2. B
    λe=4λα\lambda_e=4 \lambda_\alphaλe​=4λα​
  3. C
    λe=λα\lambda_e=\lambda_\alphaλe​=λα​
  4. D
    λe<λα\lambda_e<\lambda_\alphaλe​<λα​
View written solutionFree

Correct answer: A

de-Broglie wavelength is given by

$$\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m q V}}$$

For same potential difference

$$\begin{gathered} \lambda \propto \frac{1}{\sqrt{m q}} \\ \frac{\lambda_\alpha}{\lambda_e}=\sqrt{\frac{m_e q_e}{m_\alpha q_\alpha}} \\ \because m_\alpha \gg m_e \\ \lambda_e>\lambda_\alpha \end{gathered}$$

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