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JEE Main 2022 (25 Jul, Shift 1) · Photoelectric Effect: Einstein's Equation

Photoelectric Effect: Einstein's Equation question from JEE Main 2022 (25 Jul, Shift 1)

Q98JEE Main 2022 · 25 JUL · SHIFT 1Medium

Photoelectric Effect: Einstein's Equation

A metal exposed to light of wavelength 800 nm800\text{ nm} and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 nm500\text{ nm} is used. The workfunction of the metal is: (Take hc =1230 eV-nm= 1230\text{ eV-nm} ).

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Answer: (c)

  1. Photon energies: 1230800=1.5375\frac{1230}{800} = 1.5375 eV and 1230500=2.46\frac{1230}{500} = 2.46 eV.
  2. K=1.5375−ϕK = 1.5375 - \phi and 2K=2.46−ϕ2K = 2.46 - \phi
  3. 3.075−2ϕ=2.46−ϕ⇒ϕ=0.6153.075 - 2\phi = 2.46 - \phi \Rightarrow \phi = 0.615 eV
  4. So the answer is (c) 0.615 eV.
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