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JEE Main 2026 (4 Apr, Shift 2) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2026 (4 Apr, Shift 2)

Q12JEE Main 2026 · 4 APR · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

The de Broglie wavelength associated with an electron accelerated through a potential difference V is λe\lambda_\mathrm{e} and the de Broglie wavelength associated with a proton accelerated through the same potential difference is λp\lambda_\mathrm{p}. If their corresponding masses are mem_\mathrm{e} and mpm_\mathrm{p}, respectively, then the ratio of their de Broglie wavelengths (λeλp)\left(\frac{\lambda_e}{\lambda_p}\right) is ______.

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Answer: (a)

  1. λ=h2meV\lambda = \dfrac{h}{\sqrt{2meV}}; same charge magnitude and same VV, so λ∝1m\lambda \propto \dfrac{1}{\sqrt{m}}.
  2. λeλp=mpme\dfrac{\lambda_e}{\lambda_p} = \sqrt{\dfrac{m_p}{m_e}}
  3. So the answer is (a) mpme\sqrt{\frac{m_p}{m_e}}.
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