When 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:
When 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:
Option 1 -
1.02eV
Option 2 -
0.61eV
Option 3 -
0.52eV
Option 4 -
0.81eV
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1 Answer
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Correct Option - 2
Detailed Solution:If the work function of the metal is φ, then the kinetic energy (K.E.) of the emitted photoelectron is given by Einstein's photoelectric equation:
K.E. = hν - φ = (hc/λ) - φCase 1: λ? = 500 nm
K? = (hc/λ? ) - φCase 2: λ? = 200 nm
K? = (hc/λ? ) - φ
Given, K? = 3K?
So, (hc/λ? ) - φ = 3 * [ (hc/λ? ) - φ]
(hc/λ? ) - φ = 3 (hc/λ? ) - 3φ
2φ = 3 (hc/λ? ) - (hc/λ? )
2φ = hc * (3/λ? - 1/λ? )
φ = (hc/2) * [3/ (500 nm) - 1/ (200 nm)]
φ = (hc/2) * [ (6 - 5) / 1000 nm]
φ = hc / 2000 nm
Using hc ≈ 1240 eV&...more
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