NCERT Notes For Class 12 Physics CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER

Class 12 Physics CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER

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NCERT Notes For Class 12 Physics CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER

Class 12 Physics CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER

 

• 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.

ELECTRON EMISSION

• 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.

PHOTOELECTRIC EFFECT

• 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

Observations

• 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.

EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT

• 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.

PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT

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

EINSTEIN’S EXPLANATION OF PHOTO ELECTRIC

EFFECT

• 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.

 

PARTICLE NATURE OF LIGHT:

THE PHOTON

• 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.

WAVE NATURE OF MATTER

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.

DAVISSON AND GERMER EXPERIMENT

Aim

• To prove wave nature of electrons.

Experimental set up

Procedure

• 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.

Observation

• 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

Reason

• 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.