Photoelectric Effect



Photoelectric Effect is a well known principle of Quantum Theory, taught in the higher grades in science curriculum across the globe. Particle Nature of Electromagnetic Radiation is one of the fundamental principle on which Quantum Theory is based. This is lucidly explained by Photoelectric Effect, formulated by Einstein. The rules behind this effect can be summarized as:
1. No electrons are ejected, regardless of the intensity of the radiation, unless its frequency exceeds a threshold value characteristic of the metal.
2. The kinetic energy of the ejected electrons increases linearly with the frequency of the incident radiation but is independent of the intensity of the radiation.
3. Even at low light intensities, electrons are ejected immediately if the frequency is above the threshold.

These observations suggest that the photoelectric effect depends on the ejection of an electron when it is undergoing a collision with a particle-like projectile (the radiation) that carries enough energy to eject the electron from the metal. If we suppose that the projectile is a photon of energy hv, where v is the frequency of the radiation, then the conservation of energy requires that the kinetic energy of the ejected electron should obey

hν = φ + Kinetic Energy
hν = φ + qVs where Vs is stopping potential.
Here φ is the work function which is Planck’s constant times the threshold frequency (v0), a frequency below which the electrons cannot be ejected. Therefore,
φ = hv0
This threshold frequency is the characteristic of the metal.
Important Results:
Increasing the frequency of the incident beam, keeping the number of incident photons fixed (this would result in a proportionate increase in energy) increases the maximum kinetic energy of the photoelectrons emitted. Thus,the stopping voltage increases.
The number of electrons ejected also changes because the probability that each photon results in an emitted electron is a function of photon energy.
If the intensity of the incident radiation is increased, there is no effect on the kinetic energies of the photoelectrons.
Increase in intensity of incident beam (keeping the frequency fixed) increases the magnitude of the photoelectric current, though stopping voltage remains the same.
Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident light, but is independent of the intensity of the incident light so long as the latter is not too high.

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