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Dual Nature of Radiation and Matter · Class 12 · CBSE · Science Physics

An electron and a proton are accelerated through the same potential difference V. What is the ratio of their de Broglie wavelengths (lambdae / lambda…

Practice question from Dual Nature of Radiation and Matter (Class 12 · CBSE · Science Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-7C2BB4

An electron and a proton are accelerated through the same potential difference VV. What is the ratio of their de Broglie wavelengths (λe/λp\lambda_e / \lambda_p)?

  1. A.11
  2. B.mpme\sqrt{\frac{m_p}{m_e}}Correct answer
  3. C.memp\sqrt{\frac{m_e}{m_p}}
  4. D.mpme\frac{m_p}{m_e}

Solution

The de Broglie wavelength is given by λ=h2mQV\lambda = \frac{h}{\sqrt{2mQV}}. Since hh, QQ (magnitude of charge), and VV are the same for both, λ∝1m\lambda \propto \frac{1}{\sqrt{m}}. Therefore, λeλp=mpme\frac{\lambda_e}{\lambda_p} = \sqrt{\frac{m_p}{m_e}}.

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