NCERT Notes For Class 12 Physics CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER, (Physics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions withinside the very last asked from those. 

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  • The Maxwell’s equations of electromagnetism and Hertz experiments on the generation and detection of electromagnetic waves established the wave nature of light.
  • The discovery of X-rays by Roentgen and of electron by J. J. Thomson was important milestones in the understanding of atomic structure.
  • American physicist R. A. Millikan performed the oil-drop experiment for the precise measurement of the charge of an electron.


  • In a metal atom outermost electrons are loosely bound to the nucleus.
  • When they absorb sufficient energy from an external source the can come out of the metal surface.
  • Following are the methods of electron emission:-
  • Thermionic emission: By suitably heating, sufficient thermal energy can be imparted to the free electrons.
  • Field emission: By applying a very strong electric field (of the order of 108 V/m) to a metal, electrons can be pulled out of the metal.
  • Secondary emission: Fast moving electrons on collision with metal atoms; eject electrons by transferring their kinetic energy.
  • Photo-electric emission: When light of suitable frequency illuminate a metal surface, electrons are emitted from the metal surface.

Work function

  • The minimum energy required by an electron to escape from the metal surface is called the work function of the metal.
  • It is denoted by φ0 and measured in eV (electron volt)
  • One electron volt is the energy gained by an electron when it has been accelerated by a potential difference of 1 volt.

  • The work function (φ0) depends on the properties of the metal and the nature of its surface.


  • The phenomenon of ejection of electrons when light of suitable frequency falls on it is called photoelectric effect.
  • Photoelectric emission was discovered in by Heinrich Hertz.
  • In photoelectric effect the light energy is converted to electrical energy.
  • The photo (light)-generated electrons are called photoelectrons and the current is called photo current.
  • Substances that respond to light are called photo sensitive substances.
  • Metals like zinc, cadmium, magnesium etc respond only to ultra violet light.
  • Alkali metals such as lithium, sodium, potassium, cesium and rubidium are sensitive to visible light.

Hallwachs’ and Lenard’s observations

  • Wilhelm Hallwachs and Philipp Lenard studied photo electric effect in detail using an evacuated glass tube with two zinc plates as electrodes.

Experimental set up


  • When ultraviolet radiations were allowed to fall on the emitter plate current flows in the circuit.
  • When collector plate is illuminated no current flows.
  • When the frequency of incident radiation is less than a certain minimum value no photo electrons emission is possible. This minimum frequency is called threshold frequency.
  • Threshold frequency depends on the nature of the metal.


  • It consists of an evacuated glass/quartz tube having a photosensitive plate C and another metal plate A.
  • Monochromatic light from the source S passes through the window W and falls on the photosensitive plate C (emitter).
  • A transparent quartz window is sealed on to the glass tube, which permits ultraviolet radiation to pass through it and irradiate the photosensitive plate C.
  • The electrons are emitted by the plate C and are collected by the plate A (collector), by the electric field created by the battery.
  • The polarity of the plates C and A can be reversed by a commutator.
  • The potential difference between the emitter and collector plates is measured by a voltmeter (V) whereas the resulting photo current flowing in the circuit is measured by a microammeter (μA). Effect of intensity of light on photocurrent
  • The photocurrent increases linearly with intensity of incident light.
  • The photocurrent is directly proportional to the number of photoelectrons emitted per second.
  • Thus the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

Intensity – Photocurrent Graph

Effect of potential on photoelectric current

  • The photoelectric current increases with increase in accelerating (positive) potential.
  • The maximum value of the photoelectric current is called saturation current.
  • When negative potential is applied the photocurrent decrease rapidly and drops to zero
  • The minimum negative (retarding) potential V0 for which the photocurrent stops or becomes zero is called the cut-off or stopping potential.
  • The stopping potential is independent of intensity of radiation.

Potential –photo current graph (for different intensities with fixed frequency)

Effect of frequency of incident radiation on stopping potential

  • The stopping potential increases with frequency.

Potential –photo current graph (for fixed intensity with different frequencies)

Maximum kinetic energy of photoelectrons

  • The maximum kinetic energy of emitted photo electrons is given by

  • Where V0 – stopping potential, e- charge of electron
  • The maximum kinetic energy of photoelectrons depends on the light source and the emitter plate material, but is independent of intensity of incident radiation.
  • For a frequency ν of incident radiation, lower than the cut-off frequency ν0 , no photoelectric emission is possible even if the intensity is large. This minimum, cutoff frequency ν0, is called the threshold frequency. It is different for different metals.

Laws of Photoelectric emission

  • The photoelectric current is directly proportional to the intensity of incident light and independent of the frequency.
  • Kinetic energy of emitted photo electrons depends on the frequency and does not depend on intensity of radiation.
  • For each metal there is a threshold frequency, below which no photoelectron emission is possible.
  • The photoelectric emission is an instantaneous process.


  • The wave picture is unable to explain the most basic features of photoelectric emission.



  • Einstein explained photoelectric effect based on quantum theory.
  • According to quantum theory, light contain photons having energy hν.
  • When a photon of energy hν is incident on a metal surface, electrons are emitted.
  • A part of the photon energy is used as the work function and the remaining part of the photon energy appears as the kinetic energy of photoelectrons.

Einstein’s photoelectric equation

  • Photon Energy = Work function + maximum K.E. of photoelectron.
  • That is

hν φ= +0 Kmax

  • Thus

  • But the work function is given by φ ν0 =h 0 , where ν0 is the threshold frequency.
  • Therefore

Kmax =h(ν ν− 0)

  • This equation is the Einstein’s photo electric equation.

Frequency – stopping potential graph ( for different metals )

  • We have, the photo electric equation,

  • Also in terms of stopping potential

  • It predicts that the V0 versus ν curve is a straight line with slope = (h/e), independent of the nature of the material.

  • Thus Planck’s constant =slope X charge of electron.

work function = – (y intercept) X charge of electron.

Photoelectric cell

  • Photoelectric cell is a device used to convert light energy into electric energy using the principle of photoelectric effect.




  • In interaction of radiation with matter, radiation behaves as if it is made up of particles called photons.

Properties of Photons

  • Each photon has energy E (=hν) and momentum p (= h ν/c), and speed c, the speed of light.
  • All photons of light of a particular frequency ν, or wavelength λ, have the same energy E (=hν = hc/λ) and momentum p (= hν/c = h/λ), independent of intensity of light.
  • By increasing the intensity of light of given wavelength, there is only an increase in the number of photons per second crossing a given area, with each photon having the same energy.
  • The photon energy is independent of intensity of radiation.
  • Photons are electrically neutral and are not deflected by electric and magnetic fields.
  • In a photon-particle collision (such as photon-electron collision), the total energy and total momentum are conserved.
  • However, the number of photons may not be conserved in a collision. The photon may be absorbed or a new photon may be created.

Dual nature of radiation

  • Radiation has wave nature as well as particle nature. This is called the dual nature of radiation.


De Broglie relation

  • De Broglie found that particles of matter have wave nature.
  • The waves associated with material particles are called matter waves or De Broglie waves
  • The wave length λ associated with a particle of momentum p is given as

  • Where m is the mass of the particle and v its speed.
  • The above equation is known as the de Broglie relation and the wavelength λ of the matter wave is called de Broglie wavelength.
  • For a photon

  • Thus λ is smaller for a heavier particle ( large m) or more energetic particle (large v).
  • Consider an electron (mass m, charge e) accelerated from rest through a potential V.

De-Broglie wave length in terms of K.E. of particle

  • We have , kinetic energy

De-Broglie wavelength in terms of potential difference (voltage)

  • The K.E. of a charge moving under a potential difference of ‘V’ volts is, K qV=, where q is the charge.
  • Thus

For an electron moving under a potential difference of ‘V volt

  • The de Broglie wavelength λ of the electron is then

  • Substituting the numerical values of h, m, e, etc we get,

Matter–waves and Heisenberg’s uncertainty principle

  • According to the Heisenberg’s principle, it is not possible to measure both the position and momentum of an electron (or any other particle) at the same time exactly.

  • The matter wave associated with the electron is not extended all over space. It is a wave packet extending over some finite region of space.
  • In that case Δx is not infinite but has some finite value depending on the extension of the wave packet.



  • To prove wave nature of electrons.

Experimental set up


  • The experimental arrangement consists of an electron gun which comprises of a tungsten filament F, coated with barium oxide and heated by a low voltage power supply.
  • Electrons emitted by the filament are accelerated to a desired velocity by applying suitable potential/voltage from a high voltage power supply (H.T. or battery).
  • They are made to pass through a cylinder with fine holes along its axis, producing a fine collimated beam.
  • The beam is made to fall on the surface of a nickel crystal.
  • The electrons are scattered in all directions by the atoms of the crystal.
  • The intensity of the electron beam, scattered in a given direction, is measured by the electron detector (collector).
  • The detector can be moved on a circular scale and is connected to a sensitive galvanometer, which records the current
  • The apparatus is enclosed in an evacuated chamber.
  • By moving the detector on the circular scale at different positions, the intensity of the scattered electron beam is measured for different values of angle of scattering θ which is the angle between the incident and the scattered electron beams.
  • The variation of the intensity (I ) of the scattered electrons with the angle of scattering θ is obtained for different accelerating voltages.
  • The experiment was performed by varying the accelarating voltage from 44 V to 68 V.


  • It was noticed that a strong peak appeared in the intensity (I ) of the scattered electron for an accelarating voltage of 54V at a scattering angle θ =500


  • The appearance of the peak in a particular direction is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals.

Experimental wavelength of electron

  • The wavelength of electron can be found by Braggs equation

  • Substituting the values , the wavelength of matter waves was found to be 0.165 nm.

Theoretical (de Broglie) wave length of electron

  • The de Broglie wavelength λ associated with electrons, for V = 54 V is given by

Comparison of the results

  • Thus, there is an excellent agreement between the theoretical value and the experimentally obtained value of de Broglie wavelength.
  • Davisson- Germer experiment thus confirms the wave nature of electrons and the de Broglie relation.


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