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BITSAT 2024Paper 1
Exam
BITSAT
Year
2024
Paper
Paper 1
Subject
Chemistry
Chapter
Structure of Atom

BITSAT 2024 · Paper 1 · Chemistry · Structure of Atom

A photon of wavelength 3000 Ã… strikes a metal surface. The work...

A photon of wavelength 3000A~…3000 Ã… strikes a metal surface. The work function of the metal is 2.13 eV. What is the kinetic energy of the emitted photoelectron? (h=6.626×10−34Js)\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right)

Options

  1. A4.0 eV
  2. B3.0 eV
  3. C2.0 eV
  4. D1.0 eV

Correct answer

C. 2.0 eV

Step-by-step solution

λ=3000A~…=3×10−7m,ϕ=2.13eV\lambda=3000 Ã…=3 \times 10^{-7} \mathrm{ m}, \phi=2.13 \mathrm{eV} K.E. =hv−hv0=hv−ϕ=hcλ−ϕ=(6.626×10−34×3×108)3×10−7−(2.13×1.6×10−19)=1.98×10−253×10−7−(3.408×10−19)=(6.60×10−19)−(3.408×10−19)=3.192×10−19J=2.0eV=h v-h v_0=h v-\phi=\frac{h c}{\lambda}-\phi=\frac{\left(6.626 \times 10^{-34} \times 3 \times 10^8\right)}{3 \times 10^{-7}}-\left(2.13 \times 1.6 \times 10^{-19}\right)=\frac{1.98 \times 10^{-25}}{3 \times 10^{-7}}-\left(3.408 \times 10^{-19}\right)=\left(6.60 \times 10^{-19}\right)-\left(3.408 \times 10^{-19}\right)=3.192 \times 10^{-19} \mathrm{ J}=2.0 \mathrm{eV}
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