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PhysicsNEET 2025Matter waves and de Broglie wavelength

Dual Nature of Radiation and Matter

A photon and an electron (mass mm) have the same energy EE. The ratio λphoton/λelectron\lambda_{\text{photon}}/\lambda_{\text{electron}} of their de Broglie wavelengths is (cc is the speed of light):

  1. A.2Em\sqrt{\dfrac{2E}{m}}
  2. B.c2mEc\sqrt{2mE}
  3. C.2mc2E\sqrt{\dfrac{2mc^2}{E}}✓
  4. D.1c2Em\dfrac{1}{c}\sqrt{\dfrac{2E}{m}}

Solution

Photon: λp=hcE\lambda_p = \frac{hc}{E}. Electron: λe=h2mE\lambda_e = \frac{h}{\sqrt{2mE}}. Ratio =hcE⋅2mEh=c2mE=2mc2E= \frac{hc}{E}\cdot\frac{\sqrt{2mE}}{h} = c\sqrt{\frac{2m}{E}} = \sqrt{\frac{2mc^2}{E}}.

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