Question:
The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
Updated On: Sep 29, 2023
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Solution and Explanation
The correct answer is: No
Work function of the metal,\(ϕ_0=4.2eV\)
Charge on an electron, \(e=1.6×10^{−19}C\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Wavelength of the incident radiation, \(λ=330nm=330×10^{−9}m\)
Speed of light, \(c=3×10^8m/s\)
The energy of the incident photon is given as:
\(E=\frac{hc}{λ}\)
\(=\frac{6.626×10^{-34}×10^8}{330×10^{-9}}=6.0×10^{-19}J\)
\(=\frac{6.0×10^{-19}}{1.6×10^{-19}}=3.76eV\)
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.
Work function of the metal,\(ϕ_0=4.2eV\)
Charge on an electron, \(e=1.6×10^{−19}C\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Wavelength of the incident radiation, \(λ=330nm=330×10^{−9}m\)
Speed of light, \(c=3×10^8m/s\)
The energy of the incident photon is given as:
\(E=\frac{hc}{λ}\)
\(=\frac{6.626×10^{-34}×10^8}{330×10^{-9}}=6.0×10^{-19}J\)
\(=\frac{6.0×10^{-19}}{1.6×10^{-19}}=3.76eV\)
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.
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Concepts Used:
Photoelectric Effect
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
- h is Planck’s constant.
- ν is the frequency of the incident photon.
- W is a work function.
- E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
- The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
- There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
- The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
- The process of photo-emission is an instantaneous process.