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UNIT-VII, DUAL NATURE OF MATTER AND RADIATION, 4 MARKS, ELECTRON EMISSION:, The liberation of electrons from the surface of a substance is known as electron emission., For electron emission, metals are used because they have many free electrons., WORK FUNCTION (w0 or ϕo), The minimum energy required by the free electrons to just leave or escape (without moving in, space) from the metal surface is called Work function., The work function depends on:(i) The nature of metal and, (ii) The conditions of the metal surface, It is measured in electron volt (eV), ONE ELECTRON VOLT (1eV), It is the amount of energy acquired by an electron when it is accelerated through a potential, difference of 1V., ∴ 1eV= charge x potential difference,  1eV = 1.6 x10 -19 Cx 1V, 𝑾, ∴ 1 eV = 1.6 x 10 -19 J [ i,e V = 𝑸 ], TYPES OF ELECTRON EMMISSION., 1) Thermionic emission:, In this method, the metal is heated to sufficient temperature (2500 °C) to enable the, free electrons (to acquire energy equal to the work function of the metal ) to come out of the, metal surface., The higher the temperature, the greater is the number of electrons emitted from the metal, surface., 2) Photo electric emission:, In this method, when light of suitable frequency (called threshold frequency) is, allowed to fall on metal surface, electrons are emitted from the metal surface., 3) Field emission:, In this method, a strong electric field (i.e. a high positive voltage) of the order of 108, -1, Vm is applied at the metal surface which pulls the free electrons out of the metal surface, because of attraction of positive field. This type of electron emission is also known as cold, cathode emission., PHOTOELECTRIC EFFECT:, The phenomenon of emission of electrons from metallic surface when light (or radiation) of suitable, frequency falls on it is called photoelectric effect., PHOTOELECTRONS:, The electrons which are ejected from the metal surface during photoelectric effect is called, photoelectric electron., PHOTOELECTRIC CURRENT:, The current so formed due to the motion of ejected electrons from the metallic surface, during photoelectric effect is called photoelectric current., , Page 1 of 10

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HERTZ HALLWACHS AND LENARD’S EXPERIMENTAL STUDY OF PHOTOELECTRIC, EFFECT., , Fig:- Experiment arrangement for study of Photo Electric Effect, It consists of an evacuated glass/quartz tube having photosensitive plate c (called emitter), plate A (called collector)., When a monochromatic radiations of suitable frequency obtained from source S, after being, filtered by a filter attached on the window W, fall on the photosensitive plate c, the photoelectron, are emitted from C and are collected by the plate A, if it is kept at positive potential. The polarity of, the plates C and A can be reversed by a commutator. Thus, the plate A can be maintained at a, desired positive or negative potential with respect to emitter C., When the collector plate A is positive with respect to the emitter plate C, the electrons are, attracted to it. The emission of electrons causes flow of electric current in the circuit. The potential, difference between the emitter and collector plate is measured by a voltmeter (v) whereas the, resulting photocurrent flowing in the circuit is measured by a micro ammeter., (A) EFFECT OF INTENSITY OF LIGHT ON PHOTOCURRENT., , Fig : - Variation of Photoelectric Current with intensity of light., It is found from the above experiment that the photoelectric current varies linearly with the, intensity of the incident radiation., As the photoelectric current is directly proportional to the number of photoelectrons emitted, per second. This implies that the number of photoelectrons emitted per second is directly, proportional to the intensity of incident radiation., (B) EFFECT OF POTENTIAL OF ANODE A (COLLECTOR)w.r.t. CATHODE C, (EMMITER)ON PHOTOELECTRIC CURRENT., It is found that the photoelectric current increases with increase in positive potential, on anode or plate A (collector)., Page 2 of 10

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SATURATION CURRENT, When all the photoelectrons emitted by the emitter (i.e. by the plate C) reach the, collector plate (i.e. A), the photoelectric current attains maximum value which is known as, saturation current., STOPPING POTENTIAL, When all the polarity is reversed the electrons are repelled and only the most, energetic electrons are able to reach the collector plate A. The photocurrent is found to, decrease rapidly until is drops to zero at a certain sharp defined critical value of the negative, potential Vo on the collector plate A., For a particular frequency of incident radiation , the minimum negative (retarding), potential given to the collector plate for which the photocurrent stops or becomes zero is, called the cut- off or stopping potential (Vo)., Photoelectric current is zero when the stopping potential is sufficient to repel even, the most energetic photoelectrons or the maximum kinetic energy, so that, Kmax= eVo, 1, , mV2max=eVo, , 2, 1, mV2 max, 2, , [∵V=W/Q], , αV, , o, , The above experiment leads to the following conclusions:, 1) The photoelectrons emitted from the emitter have different kinetic energies., 2) For a given photosensitive material of emitter and frequency of incident radiation (above, threshold frequency), the value of stopping potential is independent of the intensity of, incident radiation, it means, the maximum kinetic energy of emitted photoelectrons, depends on the radiation source and nature of material of emitter but is independent of the, intensity of incident radiation., , Fig:- Variation of Photo Current with collector plate potential for different, intensity of incident radiation (same frequency), 3) EFFECT OF FREQUENCY OF INCIDENT RADIATION (SAME INTENSITY) ON, STOPPING POTENTIAL., , Page 3 of 10

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From the graph we note that,, i), The value of stopping potential is different for radiation of different frequency., ii), The value of stopping potential is more negative for radiation of higher incident, frequency., iii), The value of saturation current depends on the intensity of incident radiation but is, independent of the frequency of the incident radiation., , Fig: - Variation of stopping potential V0 with frequency v of incident radiation for a given, photosensitive material., The graph shows that, 1. The stopping potential Vo varies linearly with the frequency of incident radiation for a, given photosensitive material., 2. There exists a certain minimum cut-off frequency vo called threshold frequency for, which the stopping potential is zero., 3. The maximum kinetic energy of the photoelectrons varies linearly with the frequency, of incident radiation, but is independent of its intensity., 4. For a frequency v of incident radiation, lower than the cut-off frequency vo, no, photoelectric is possible even if the intensity is large., LAWS OF PHOTOELECTRIC EMISSION., 1. For a given photosensitive material and frequency of incident radiation (above the, threshold frequency), the number of photoelectron ejected per second or the, photoelectric current is directly proportional to the intensity of incident light., 2. For a given photosensitive material and frequency of incident radiation, saturation, current is found to be proportional to the intensity of incident radiation whereas the, stopping potential is independent of its intensity., 3. For a given photosensitive material, there exists a certain minimum cut-off frequency of, the incident radiation called the threshold frequency, below which no emission of, photoelectrons takes place, no matter how intense the incident light is., 4. Above the threshold frequency, the stopping potential or the maximum kinetic energy of, the emitted photoelectrons is directly proportional to the frequency of the incident light, but it is independent of the intensity of the incident light., 5. The photoelectric emission is an instantaneous process. The time lag between the, incidence of radiation and emission of photoelectrons is very small, less than even 10-9, sec., SURFACE BARRIER OF ELECTRON, As soon as an electron tends to leave the metal surface, a positive charge is, developed on the surface of the metal. This positive charge pulls back the free electron, Page 4 of 10

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tending to leave the metal surface. This attracting force is called restraining force causing, potential barriers or surface barriers of electron., EINSTIEN’S PHOTOELECTRIC EQUATION, Einstein’s proposed a theory based upon Planck’s hypothesis. Planck postulated that, light wave consist of tiny bundles of energy called quanta or photons., The energy of each photon is E= hv where h is the Planck’s constant and v is the frequency, of the incident photon., Einstein assumes that one photoelectron is ejected from a metal surface if one, photon of suitable light radiation falls on it., According to Einstein’s when a photon of energy hv falls on a metal surface, the, energy of the photon is absorbed by the free electron in the metal. This absorbed energy (hv), is utilised in two ways., 1. A part of energy is used by the electrons to overcome the surface barrier to come out of, the metal surface. This part of the energy is equal to the work function (ϕo ) of the, metal., 2. The remaining part of the energy is used in giving a velocity to the emitted, photoelectron. This part of the energy is equal to the maximum kinetic energy of the, 1, emitted photoelectron i.e. 2mv2max, 1, , i.e. hv = ϕo + mv2max, 2, , Q. Derive Einstein’s photoelectric emission., Let v and vo be the frequency of incident light and the threshold frequency., According to Einstein’s, Energy of photon =Work Function +K.E of an Electron, 𝟏, hv= ϕo + 𝟐mv2---------------------------------(1), If v=vo , then electron will not be emitted from metal surface, 𝟏, , i.e. 𝟐mv2 = 0, then, eqn (1) becomes, hv =ϕo, ------------------------------------------------(2), which is the expression for work function., Again eqn (1) becomes, 𝟏, hv = hvo + 𝟐mv2, 𝟏, , mv2= h(v-vo ), i.e. Kmax = h(v-vo )--------------------------------(3), Then eqn. (3) is called Einstein’s photoelectric equation,, NOTE, From Einstein’s photoelectric equation, Kmax= hv - ϕo, [ i.e. ϕo=hvo], i. If hv <ϕo or v< vo then Kmax is negative which is impossible. Therefore, photoelectric, emission cannot occur if the frequency of incident radiation is less then vo ., ii. If hv >ϕo or v> vo , then Kmax is non-negative, this means that maximum K.E. of, photoelectrons depends only on the frequency(v ) of the incident radiation., iii. According to Einstein’s equation:, Kmax = hv - ϕo, 𝟐, , 𝟏, , mv2max = hv - ϕo, eVo = hv - ϕo[ i,e 𝟏𝟐mv2max = eVo], 𝟐, , Page 5 of 10

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𝒉, , 𝝓𝒐, , Vo = 𝒆 v - 𝒆 ----------------------------------------(i), n, Eq (1) is the equation of a straight line, therefore, graph between v and Vo is a straight, line., Comparing eqn (1) with the standard equation of a straight line y = mx+c,, We have,, 𝒉, Slope of graph, m = 𝒆, , Fig : - Frequency stopping potential graphs for two metals A and B., 𝒉, The graph are parallel straight lines. It is because the slope of each graph is the same (= 𝒆 ), but the threshold frequency is diffrent for diffrent metals., , Particle nature of lights:, In 1905, Einstein proposed a new theory of light called photon theory of light. According to photon, theory of light, light waves or electromagnetic waves consist of tiny packets of energy called, photons., The photon theory suggests that light is not emitted continuously as waves instead or photons. Since, a photon has energy as well as momentum, it behaves as particle., , Properties of photon:, 1. In interaction of radiation with matter, radiation behaves as if it is made particles like, photon., 2. Energy of each photon, E = hv, 𝑪, , 3. Wavelength of photon, λ = 𝒗, 𝒉𝒗, , 4. Mass of photon, m = 𝑪𝟐, , 5. Momentum of photon, p =, , 𝒉𝒗, 𝑪𝟐, 𝒉𝒗, , xC, , = 𝑪, 6. All the photons emitted from a source of radiations travel through apace withy the same, speed C, equal to the speed of light., 7. Photons are electrically neutral., 8. They can’t be defeated by electric and magnetic fields., 9. 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., 10. The rest mass of a photon is zero., Page 6 of 10

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From , m=, , 𝑚𝑜, 2, √1− 𝑣2, 𝑐, , m0 = m √1 −, , , which mo is rest mass of photon, 𝑣2, 𝑐2, , Since, 𝑣 2 = C, , ∴ mo = 0, Q. Discuss dual nature of radiation?, According to the wave theory, the radiant energy sprayed out continuously in the form of, wave but in a phenomenon like photoelectric effect when a single photon of radiation of, sufficient energy strikes a metal surface, electron is emitted. It is cleared that a particle i.e. ,, photon of radiation is colliding against another particle i.e. electron . it shows that radiation, passes particle natured. Thus, radiation behaves sometimes as waves and sometimes as particle., Thus, it is said to have dual nature., Q. What led Louis de- Broglie to put forward the duality hypothesis for matter both i.e. the, material particle can behave both as wave as well as particle?, Following assumptions lead him to the duality hypothesis for matter., i., The universe is made of particles, ii., Nature loved symmetry, as the radiations have got dual nature, matter should also posses, dual nature., De- Broglie hypothesis:, According to de- Broglie a moving material particle sometimes acts as a wave and, sometimes as a particle or a wave is associated with moving particle which controls the particle in, every respect., De- Broglie waves or matter waves:, The waves associated with moving materials particles are known as De- Broglie waves or, matter waves., De- Broglie wavelength (λ):, The length of de- Broglie waves or matter waves is known as de- Broglie wavelength., , # Derivation of de- Broglie wave length:, We know that energy of a photon is given by, E = hv, According to Einstein mass energy equivalent the energy of the photon is., E=mc2 ------------------------ (2), where m= the mass of the photon and, C= the speed of light., n, From eq (1) & (2),, , mc2 = hv, mc2 = h, , λ=, , 𝑪, 𝛌, , 𝒉, 𝐦𝐜, Page 7 of 10

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λ=, , 𝒉, , , where p = mc, momentum of photon, , 𝐩, , If instead of a photon, we consider a material Particle ‘m’ moving with velocity ‘v’ , then, equation (3) becomes, , λ=, , 𝒉, , , which is the expression for de- Broglie wavelength, 𝒎𝒗, De- Broglie wavelngth of an electron moving through a potential difference:, `, , Let us consider an electron of mass ‘m’ and charge ‘c’. Let ‘v’ be the velocity acquired by, electron when accelerated form rest through a potential difference of ‘v’ volt., Then,, 𝟏, K.E. acquired by an electron = 𝟐mv2, But,, , 𝟏, , mv2= eV, mv2=2eV, 𝟐, , (𝑚v2 ), 𝑚, , = 2eV, , mv = √2𝑒𝑉𝑚, But,, , λ=, , ℎ, , 𝑚𝑣, , 𝒉, , λ = √𝟐𝒎𝒆𝑽, 𝒉, , λ = √𝟐𝒎𝑬, , ,[i.e. E = eV], , Substituting the numerical values of h, m, e, 𝟏.𝟐𝟐𝟕, λ = √𝟐𝑽 Å, Note, From de-Broglie hypothesis, we conclude that, De- Broglie wave length, λ =, , ℎ, 𝑚𝑣, , If v = 0, λ = ∞, And v = ∞, λ = 0, i. It means the matter waves are associated with material particles only if they are in motion., ii. The intensity of a matter wave at a point, represents the probability of the associated, particle (eg. electron) being there. Therefore if, the intensity of matter wave is large in a, certain region, there is a greater probability of, the particle being found there., Photoelectric cell (or photo tube), It is a device which converts light energy into, electrical energy., Application of photo electric cells., i., These are used in television camera for telecasting scenes and in photo telegraph., ii., These are used to switch on and off the street lighting system at dusk and dawn without, any manual attention., iii., They are used to measure the temp/ of stars and to study the spectrum of the heavenly, bodies., iv., They are used for the determination of Planck’s bodies, v., They are used in industries for locating minor flows or holes in metallic sheets., Page 8 of 10

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EXPERIMENTAL DEMONSTRATION OF WAVE NATURE OF ELECTRON, The wave nature of slow moving electrons has been established experimentally by Davisson and, Germer in 1927., The apparatus as shown in Figure below consists of a filament F of tungsten coated with, barium oxide, which on heating with current from low tension battery emits large number of, electrons. C is a hollow metallic cylinder with a hole along the axis, it surrounds the filament and, is kept at negative potential, so that the electrons emitted from filament may form a, convergent beam of electron. It acts as a cathode. A is a cylinder with fine hole along its axis. It, is kept at positive potential w.r.t. cathode and is called anode. The cathode and anode form, an electron gun, by which a fine beam of electrons can be obtained under different, accelerating potentials applied between cathode and anode. TV is a nickel crystal cut along, cubical diagonal. D is an electron detector. It can be rotated on a circular scale and is connected, to a sensitive galvanometer which records the current., , Working. A fine beam of accelerated electrons obtained from electron gun is made to fall, normally on the surface of nickel crystal. The incident electrons are scattered in different, directions by the atoms of the crystal. The intensity of the electron beam, scattered in a given, direction is found by the use of detector. By rotating the electron detector on circular scale at, different positions, the intensity of the scattered beam is measured for different values of, scattering angle (p, the angle between the incident and the scattered electron beam., The experiment was performed by varying the accelerating voltage from 44 V to 68 V. It was, noticed that at accelerating voltage 54 V, the variation of intensity (/) and scattering angle (cp), is of the type as shown in Figure below : -, , Page 9 of 10

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50°, , From the graph, it is noted that at accelerating voltage 54 V, there is a sharp peak in the intensity, of the scattered electrons for scattering angle 𝝓 = 50°., The appearance of peak in a particular direction is due to constructive interference of, electrons scattered from different layers of regularly spaced atoms of the crystal, i.e., the, diffraction of electrons takes place. This establishes the wave nature of electron., From Figure below we note that for the scattering angle 𝝓 = 50°, the angle of glancing (angle, between the scattered beam of electron with the plane of atoms of the crystal), (0) for the, electron beam will be given by, , This shows that there is a close agreement with the estimated value of de Broglie wavelength, and the experimental value determined by Davisson and Germer. This proves the existence of de, Broglie waves for the slow moving electrons., The wave nature of fast moving electrons was established by G.P. Thomson with his, experiment, named G.P. Thomson's experiment., , Page 10 of 10