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Light of wavelength 200 Å fall on aluminium surface. Work function of aluminium is 4.2 eV.
What is the kinetic energy of the fastest emitted photoelectrons?
  • a)
    2 eV
  • b)
    1 eV
  • c)
    4 eV
  • d)
    0.2 eV
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Light of wavelength 200 Å fall on aluminium surface. Work function of...
By Einstein’s equation of photo-electric effect, the maximum kinetic energy of emitted photo-electrons is given by
Where, h = Planck’s constant
v = frequency of incident light
W = work function of metal
λ = wavelength of incident fight
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Community Answer
Light of wavelength 200 Å fall on aluminium surface. Work function of...

Calculation of Kinetic Energy of the Fastest Emitted Photoelectrons:

- Given:
- Wavelength of light (λ) = 200 Å = 200 x 10^-10 m
- Work function of aluminium (Φ) = 4.2 eV
- Energy of a photon (E) = hc/λ, where h = Planck's constant and c = speed of light
- Calculate the energy of a photon:
- E = (6.626 x 10^-34 J.s x 3 x 10^8 m/s) / (200 x 10^-10 m) = 9.939 x 10^-19 J
- Convert the energy of a photon to eV:
- E = 9.939 x 10^-19 J x (1 eV / 1.602 x 10^-19 J) = 6.21 eV
- Calculate the kinetic energy of the fastest emitted photoelectrons:
- Kinetic Energy = Energy of a photon - Work function
- Kinetic Energy = 6.21 eV - 4.2 eV = 2.01 eV

Therefore, the kinetic energy of the fastest emitted photoelectrons is 2 eV, which corresponds to option 'A'.
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