Question
Download Solution PDFWhen the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Let the work function of the metal be φ, and let the initial wavelength be λ1 = 500 nm and the final wavelength be λ2 = 200 nm. The energy of the photon is given by:
E = h× c / λ
where:
- h = Planck's constant
- c = speed of light
- λ = wavelength
Initially, the kinetic energy of the photoelectron is:
K.E. = E1 - φ = h × c / λ1 - φ
Finally, the kinetic energy becomes three times larger:
3 × K.E. = E2 - φ = h × c / λ2 - φ
From the ratio of the kinetic energies:
3 × (h × c / λ1 - φ) = h × c / λ2 - φ
Solve for φ (work function of the metal):
φ ≈ 0.61 eV
The correct answer is: 0.61 eV
Last updated on Jun 6, 2025
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