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Dual Nature of Radiation question

2025 · 7 Apr · Shift 2 · Q52
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Dual Nature of Radiation question

2025 · 7 Apr · Shift 2 · Q52

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
A photoemissive substance is illuminated with a radiation of wavelength λi\lambda_iλi​ so that it releases electrons with de-Broglie wavelength λe\lambda_eλe​. The longest wavelength of radiation that can emit photoelectron is λo\lambda_oλo​. Expression for de-Broglie wavelength is given by: (m: mass of the electron, h: Planck's constant and c: speed of light)
  1. A
    λe=hλi2mc\lambda_e = \frac{\sqrt{h \lambda_i}}{\sqrt{2mc}}λe​=2mc​hλi​​​
  2. B
    λe=h2mc(1λi−1λo)\lambda_e = \frac{h}{\sqrt{2mc \left( \frac{1}{\lambda_i} - \frac{1}{\lambda_o} \right)}}λe​=2mc(λi​1​−λo​1​)​h​
  3. C
    λe=h2mc(1λi−1λo)\lambda_{\mathrm{e}}=\sqrt{\frac{\mathrm{h}}{2 \mathrm{mc}\left(\frac{1}{\lambda_i}-\frac{1}{\lambda_{\mathrm{o}}}\right)}}λe​=2mc(λi​1​−λo​1​)h​​
  4. D
    λe=hλ02mc\lambda_e=\sqrt{\frac{h \lambda_0}{2 m c}}λe​=2mchλ0​​​
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