Revision: Dual Nature of Radiation and Matter >> Photoelectric Effect Physics (Theory) ISC (Science) ISC Class 12 CISCE

The phenomenon of emission of electronsfrom metals under the effect of light is called 'photoelectric effect'.

The minimum energy required for the emission of photoelectron from a metal is called the 'work function' of that metal.

The negative potential of P₂ (relative to P₁) at which the photoelectric current becomes zero is called 'stopping potential' or 'cut-off potential'.

The lowest frequency of light which can emit photoelectrons from a material is called the 'threshold frequency' or 'cut-off frequency' of that material.

The energy crossing per unit area per unit time perpendicular to the direction of propagation of wave is called the intensity of wave.

n = \[\frac {Pλ}{h c}\]

m = \[\frac {E}{c^2}\] = \[\frac {hv}{c^2}\] = \[\frac {h}{cλ}\]

p = \[\frac {E}{c}\] = \[\frac {h}{λ}\]

P = nh\[\frac {c}{λ}\]

1. The rate of emission of photoelectrons from the surface of a metal varies directly as the intensity of the incident light falling on the surface.
2. The maximum kinetic energy of the emitted photoelectrons is independent of the intensity of the incident light.
3. The maximum kinetic energy of the photoelectrons increases linearly with an increase in the frequency of the incident light.
4. If the frequency of the incident light is below a certain lowest value, then no photoelectron is emitted from the metal. This lowest frequency (threshold frequency) is different for different metals.
5. As soon as the light is incident on the surface of the metal, the photoelectrons are emitted instantly; that is, there is no time-lag between the incidence of light and the emission of electrons.

• Hertz (1887) observed that ultraviolet light makes electric discharge easier from a metal surface.
• Hallwachs’ experiment showed that current flows only when ultraviolet light strikes the negative plate, not the positive plate.
• J.J. Thomson (1898) proved that light falling on a metal surface causes the emission of electrons.
• Lenard (1900) explained that electrons emitted from the negative plate are attracted to the positive plate, producing current.
• Short-wavelength (high-frequency) light is more effective in producing photoelectric emission than long-wavelength light.

• Photoelectric current increases with incident light intensity when the frequency is kept constant.
• For sufficiently high anode potential, the photoelectric current reaches a maximum (saturation current).
• Stopping potential is independent of light intensity and depends on the maximum kinetic energy of photoelectrons.
• A higher frequency of incident light produces photoelectrons with greater maximum kinetic energy.
• No photoelectric emission occurs below a certain frequency, regardless of the intensity or duration of light.

• A graph of stopping potential V_0​ versus frequency ν is a straight line, showing a linear relation between them.
• The slope of the V₀ – ν graph equals h/e, hence Planck’s constant h can be determined using the known value of electronic charge e.

• Radiation behaves like a stream of particles called photons during interaction with matter.
• Photons travel in straight lines at the speed of light.
• Each photon has energy E = hν = \[\frac {hc}{λ}\]​ and momentum p = \[\frac {E}{c}\].
• On a change of medium, the speed and wavelength of a photon change, but its frequency remains constant.
• Photon energy is independent of light intensity; higher intensity means more photons per second.
• A photon has zero rest mass, but an equivalent mass given by
• m = \[\frac {h}{cλ}\]​
• Photons are electrically neutral and are not deflected by electric or magnetic fields.
• In photon–particle collisions, total energy and momentum are conserved.
• A photon retains its identity until absorbed by an atom, after which its identity is lost.

• Wave theory fails because it predicts that electron energy should increase with light intensity, but experiments show that it does not.
• Wave theory cannot explain the existence of a threshold frequency, below which no photoelectrons are emitted.
• Wave theory predicts a time lag in emission, but photoelectrons are emitted instantaneously.

• Wave theory failed to explain experimental observations of the photoelectric effect.
• Black-body radiation contains all wavelengths, and classical theories could not explain its energy distribution.
• Planck proposed that radiation is emitted discontinuously in small energy packets, now known as quanta (photons).
• The energy of a photon is hνh\nuhν, and radiation energy is emitted only in integral multiples of hνh\nuhν.
• Einstein (1905) explained the photoelectric effect using Planck’s photon hypothesis.

• Light consists of photons, each having energy hνh\nuhν; light intensity depends on the number of photons.
• A photon transfers its entire energy to a single electron during photoelectric emission.
• Part of the photon energy is used to overcome the work function, and the rest appears as kinetic energy of the electron.
• Electrons emitted from the metal surface have maximum kinetic energy because they experience no energy loss in collisions.
• Einstein’s photoelectric equation is
  E_k = hν − W = h(ν − ν₀)
• Increasing light intensity increases the number of photoelectrons, but not their maximum kinetic energy.
• Photoelectric emission is instantaneous, and Einstein’s explanation fully accounts for all laws of the photoelectric effect.