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Question

Physics Question on Dual nature of radiation and matter

The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

Answer

The correct answer is: No
Work function of the metal,ϕ0=4.2eVϕ_0=4.2eV
Charge on an electron, e=1.6×10−19Ce=1.6×10^{−19}C
Planck’s constant, h=6.626×10−34Jsh=6.626×10^{−34}Js
Wavelength of the incident radiation, λ=330nm=330×10−9mλ=330nm=330×10^{−9}m
Speed of light, c=3×108m/sc=3×10^8m/s
The energy of the incident photon is given as:
E=hcλE=\frac{hc}{λ}
=6.626×10−34×108330×10−9=6.0×10−19J=\frac{6.626×10^{-34}×10^8}{330×10^{-9}}=6.0×10^{-19}J
=6.0×10−191.6×10−19=3.76eV=\frac{6.0×10^{-19}}{1.6×10^{-19}}=3.76eV
It can be observed that the energy of the incident radiation is less than the work function of the metal.Hence,no photoelectric emission will take
place.