How many of the given metals will show photoelectric effect when light of 400 nm falls on below metal? Metal Li Na K Mg Cu Ag W(eV) 2.42 2.3 2.25 3.7 4.8 4.3:
Solution and Explanation
The correct answer is : 3
The photoelectric effect requires a photon with energy greater than the work function of the metal.
A photon's energy is provided by
\(E=\frac{hc}{\lambda}\)
Where,
h = Planck's constant, c = Velocity of light, λ = Wavelength
here given λ = 400 nm
Then E = \(\frac{6.6\times10^{-34}\times3\times10^8}{400\times 10^{-9}}\)
E in e.V = \(\frac{6.6\times10^{-34}\times3\times10^8}{400\times 10^{-9}\times1.6\times10^{-19}}\)
E = 3 eV
The metals Li, Na, K and Mg have a work function less than the Energy of a Photon. In the presence of light with a wavelength of 400nm, they exhibit a photoelectric Effect.
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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.