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.
- 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.
- 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.
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
- 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
- But the work function is given by φ ν0 =h 0 , where ν0 is the threshold frequency.
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 is a device used to convert light energy into electric energy using the principle of photoelectric effect.
PARTICLE NATURE OF LIGHT:
- 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.
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
- 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.