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JEE Main 202229 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2022 · 29 June · Evening Shift · Physics · Dual Nature of Matter

The electric field at a point associated with a light wave is given...

The electric field at a point associated with a light wave is given by
E=200[sin⁡(6×1015)t+sin⁡(9×1015)t]Vm−1E = 200\left[\sin \left(6 \times {10}^{15}\right)t + \sin \left(9 \times {10}^{15}\right)t\right]{Vm}^{- 1}

Given: h=4.14×10−15eVsh = 4 . 14 \times {10}^{- 15}eVs

If this light falls on a metal surface having a work function of 2.50eV2 . 50eV, the maximum kinetic energy of the photoelectrons will be

Options

  1. A1.90eV1 . 90eV
  2. B3.27eV3 . 27eV
  3. C3.60eV3 . 60eV
  4. D3.42eV3 . 42eV

Correct answer

D. 3.42eV3 . 42eV

Step-by-step solution

Given: E=200[sin⁡(6×1015)t+sin⁡(9×1015)t]Vm−1E = 200\left[\sin \left(6 \times {10}^{15}\right)t + \sin \left(9 \times {10}^{15}\right)t\right]V{m}^{- 1}

Here, angular velocity, ω1=6×1015{\omega}_{1} = 6 \times {10}^{15}and ω2=9×1015{\omega}_{2} = 9 \times {10}^{15}

Maximum kinetic energy of the photoelectron is KEmax.=E−ϕ{KE}_{max .} = E - ϕ

=hf−ϕ=hω2π−ϕ= hf - ϕ = \dfrac{h\omega}{2\pi} - ϕ

=4.14×10−15×9×10152×3.14−2.5=5.92−2.50=3.42eV= \dfrac{4 . 14 \times {10}^{- 15} \times 9 \times {10}^{15}}{2 \times 3 . 14} - 2 . 5 = 5 . 92 - 2 . 50 = 3 . 42eV

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