Dual nature of radiation and matter class 12

Chapter 12th of NCERT book of class 12. Whole syllabus has been covered.

1. DUAL NATURE OF RADIATION AND MATTER Lect. Lovedeep Singh

2. ORIGIN OF THEORY The idea of duality originated in a debate over the nature of light and matter that dates back to the 17 th century, when competing theories of light were proposed by Christian Huygens and Isaac Newton: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie,Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have wave nature (and vice versa).

3. The phenomenon such as interference, diffraction, polarization etc. in which radiation interacts with radiation itself can be explained on the basis of electromagnetic (wave) nature of radiation only. The phenomenon such as photoelectric effect, compton effect, pair production etc. in which radiation interacts with matter can be explained on the basis of quantum (particle) nature of radiation only. The phenomenon such as reflection, refraction, dispersion etc. in which radiation interacts neither with radiation itself nor matter can be explained on the basis either of two natures of radiation. INTRODUCTION

4. ELECTRON EMISSION The ejection of electrons from the surface of a metal is known as Electron Emission . We know that every metal has free electrons . These electrons are free to the extent that they may transfer from one atom to another within the metal but they cannot leave the metal surface to provide electron emission because of electrostatic attraction of positive nuclei inside the atom. However, if sufficient energy is given to the free electrons, their kinetic energy increases and thus the electrons will cross over the surface barrier to leave the metal. Work function ( ф ): The minimum energy required by an electron to just escape (i.e. with zero velocity) from metal's surface is called Work function (ф ) of the metal . The work function of pure metals varies (roughly) from 2eV to 6eV. 1 eV = 1.602 ×10 -19 J

5. METHODS OF ELECTRON EMISSION ( i ) Thermionic emission: In this method, the metal is heated to a sufficient temperature (about 2500 C) to enable the free electrons to leave the metal surface. The number of electrons emitted depends upon the temperature. The higher the temperature, the greater is the emission of electrons. The ejected electrons are called thermal electrons. (ii) Field emission: In this method, a strong electric field (i.e. a high positive voltage) is applied at the metal surface which pulls the free electrons out of the metal because of the attraction of positive field. The strong the electric field, the greater is the electron emission. The ejected electrons are called field electrons. (iii) Photoelectric emission: In this method, the energy of light falling upon the metal surface is transferred to the free electrons within the metal to enable them to leave the surface. The greater the intensity of light beam falling on the metal surface, the greater is the photoelectric emission. The ejected electrons are called photoelectrons. (iv) Secondary emission: In this method, a high velocity beam of primary electrons strikes the metal surface. The intensity of secondary emission depends upon the emitter material, mass and energy of bombarding particles. The ejected electrons are called secondary electrons.

6. Photoelectric effect The phenomena of emission of electrons from a metal surface, when radiations of suitable frequency is incident on it, is called photoelectric effect . The electrons emitted by this effect are called photoelectrons and the current constituted by photoelectrons is known as photoelectric current or photocurrent. It was discovered by Heinrich Hertz in 1887 during his EM waves experiments. Threshold Frequency ( v o ): The minimum frequency of light which can eject photo electron from a metal surface is called threshold frequency of that metal. Threshold Wavelength ( λ max ): The maximum wavelength rJ light which can eject photoelectron from a metal surface is called threshold wavelength of that metal. Relation between work function, threshold frequency and threshold wavelength φ = hv o = hc / λ max

7. EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT Philipp Lenard studied the photoelectric effect practically. Fig. shows his experimental setup C – Metallic cathode A – Metallic Anode W – Quartz Window When light of suitable frequency falls on the metallic cathode, photoelectrons are emitted. These photoelectrons are attracted towards the + ve anode and hence photoelectric current is constituted.

8. Effect of Intensity on Photocurrent Current is number of electrons passing through a cross section in unit time . As Intensity ↑ →No of electron emitted ↑ → Current ↑ Photocurrent ∝ Intensity

9. Effect of collector potential Collector potential is meant for collecting emitted electrons . Current first increases with increase in collector potential after which it saturates. It saturates (become constant ) when emitted electrons = collected electrons. This maximum current is called saturated current . Now If we keep voltage negative , it will repel electrons . At some potential, all electrons will get repelled . At this potential , Photocurrent will be zero . This is called stopping potential. eVstopping = KEmax KE max = hv – eVstopping = hv – ф Vstopping = ( hv – ф )/ e So stopping potential depends on frequency and work function .

10. Effect of frequency For a fixed intensity of incident light, the photo electric current does not depend on the frequency of the incident light. Saturation current will be same for all frequencies> Threshold frequency The graph between frequency and stopping potential is always a st . line and implies that there is always a minimum frequency below which there is no photocurrent.

11. Laws of Photoelectric Effect 1. For a given metal and frequency of incident light, the photo electric current (the rate of emission of photoelectrons) is directly proportional to the intensity of incident light. 2. For a given metal, there is a certain minimum frequency, called threshold frequency, below which there is no emission of photo electrons takes place. 3. Above threshold frequency the maximum kinetic energy of photo electrons depends upon the frequency of incident light. 4. The photoelectric emission is an instantaneous process. i.e. as soon as the photon of suitable frequency falls on the substance, it emits photoelectrons.

12. EINSTEIN'S PHOTOELECTRIC EQUATION According to Plank's quantum theory , light is emitted from a source in the forms of bundles of energy called photons . Energy of each photon is E= h ν . Einstein made use of this theory to explain how photo electric emission takes place. According to Einstein, when photons of energy fall on a metal surface, they transfer their energy to the electrons of metal. i ) A part of this energy is used to overcome the surface barrier and come out of the metal surface. This part of the energy is called ‘work function’ ( ф = hv o ). ii)The remaining part of the energy is used in giving a velocity ‘v’ to the emitted photoelectron. This is equal to the maximum kinetic energy of the photoelectrons (½ mv 2 max ) where ‘m’ is mass of the photoelectron.

13. EINSTEIN'S PHOTOELECTRIC EQUATION According to law of conservation of energy, energy of photon= work function+ K.E. imparted to electron h ν = ф + ½ mv 2 max = hv o + ½ mv 2 max K max =h ( ν- v o ) This relation is called Einstein’s photoelectric equation.

14. Verification of Laws of Photoelectric Emission based on Einstein’s Photoelectric Equation: i ) If ν < v o , then ½ mv 2 max is negative, which is not possible. Therefore, for photoelectric emission to take place ν > v o . ii) Since one photon emits one electron, so the number of photoelectrons emitted per second is directly proportional to the intensity of incident light. iii) It is clear that ½ mv 2 max is proportional to ν as h and v o are constant. This shows that K.E. of the photoelectrons is directly proportional to the frequency of the incident light. iv) Photoelectric emission is due to collision between a photon and an electron. As such there can not be any significant time lag between the incidence of photon and emission of photoelectron. i.e. the process is instantaneous. It is found that delay is only 10 -8 seconds.

15. Applications of photoelectric effect PHOTOCELL A device which converts light energy into electrical energy is called photoelectric cell. It is also called as photocell or electric eye . When a radiation of suitable frequency is made to fall on cathode, photoelectrons are emitted, which are attracted by the anode. Anode is kept at positive potential with respect to cathode . This arrangement results in the flow of current when the radiation falls on the metal surface . This current can be measured using the micro ammeter .

16. Applications of the photoelectric cells Photoelectric cells are used in the television camera for telecasting scenes and are also used in the photo-telegraphy. Photocells are used for sound recording and video recording. It is used in the counting machines. It is used in burglar alarms and fire alarms. Photocells are also used to measure the temperature of stars and study their spectrum. They are used to switch on and off the streetlight without any manual attention. They are used in the photometry to compare the illuminating powers of the two sources. They are used for the determination of the Planck’s constant. They are used to control the temperature of the chemical reactions. They are used to sort out the materials of different shades. They are used to determine the opacity of solids and liquids. They are used to locate minor flaws in metallic sheets.

17. Photons- Packets of energy 1 . Electrically neutral , No effect of Electric field or magnetic field 2 . Massless 3 . Energy E = h ν = hc / λ & Momentum p = h/ λ 4.Energy and Momentum depends only on Frequency (or wavelength). 5.When photon collides with particle, then Total momentum will remain conserved like any other normal collision .But some photos may die in collision (Number of photon may change after Collison ) 6. All photons possess same energy irrespective of intensity of light. Increase in intensity only increases the no. of photons.

18. de Broglie wave According to de Broglie, a moving material particle can be associated with a wave. i.e. a wave can guide the motion of the particle. The waves associated with the moving material particles are known as de Broglie waves or matter waves. Expression for de Broglie wave: λ According to quantum theory, the energy of the photon is E = hν = hc / λ According to Einstein’s theory, the energy of the photon is E = mc 2 So, or where p = mc is momentum of a photon If instead of a photon, we have a material particle of mass m moving with velocity v, then the equation becomes λ = h/ mv which is the expression for de Broglie wavelength

19. de Broglie wavelength for electron As studied previously, de Broglie is given by or The kinetic energy is related to momentum as For electron Charge (e), kinetic energy is K = eV For Electrons only

20. conclusion i ) de Broglie wavelength is inversely proportional to the velocity of the particle. If the particle moves faster, then the wavelength will be smaller and vice versa. ii) If the particle is at rest, then the de Broglie wavelength is infinite. Such a wave can not be visualized. iii) de Broglie wavelength is inversely proportional to the mass of the particle. The wavelength associated with a heavier particle is smaller than that with a lighter particle. iv) de Broglie wavelength is independent of the charge of the particle. Matter waves, like electromagnetic waves, can travel in vacuum and hence they are not mechanical waves. Matter waves are not electromagnetic waves because they are not produced by accelerated charges.

21. Davisson and Germer Experiment The Davisson– Germer experiment was a physics experiment conducted by American physicists Clinton Davisson and Lester Germer in 1927, which confirmed the de Broglie hypothesis. This hypothesis advanced by Louis de Broglie in 1924 says that particles of matter such as electrons have wave like properties. The experiment not only played a major role in verifying the de Broglie hypothesis and demonstrated the wave-particle duality, but also was an important historical development in the establishment of quantum mechanics and of the Schrödinger equation . A beam of electrons emitted by the electron gun is made to fall on Nickel crystal cut along cubical axis at a particular angle. The scattered beam of electrons is received by the detector which can be rotated at any angle. The energy of the incident beam of electrons can be varied by changing the applied voltage to the electron gun. Intensity of scattered beam of electrons is found to be maximum when angle of scattering is 50 ° and the accelerating potential is 54 V.