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Dual nature of radiation and matter |, , Free electrons in metals, , Ques.- Why do metals have large number of free electrons? Define work function of metals., , Ans.-In metals, the electrons in the outermost shells of, the atoms are very loosely bound to their nuclei. It is because of weak electrostatic force of attractions between, these electrons and the nucleus. As a result, some of them, leave their parent atoms and move about freely in a random fashion within the metal. These are called free electrons. At an ordinary temperature, the free electrons in, metals cannot leave the surface of metal. It is because, they are attracted by the positive ions., , Thus, free electrons require certain energy to overcome the binding force ie the surface barrier and escape, from the metal surface. This is called the work function of, metal and the phenomenon is called electron emission., , Hence work function of a metal is defined as the, minimum energy required by a free electron to just escape, or leave metal surface without imparting it any kinetic energy)., , The value of work function is different for different, metals. Its value is maximum for platinum (5.65 eV) and, minimum for caesium (2.14 eV), , Electron emission, , Ques.- Explain briefly the different methods of electron, emission, , Ans.- The phenomenon of emission of electrons from the, surtace.of a metal is called electron emission., , The electron emission from metal surfaces can take, place in following ways., (1) Thermoinic emission- The emission of electrons froma, metal surface when it is heated to suitable high temperature ts called thermionic emission. The electrons so emitted are called thermions or thermal electrons and the metal, surfaces is called an emitter or cathode., (ii) Photoelectric emission-The emission of electrons from, a metal surface when light of suitable freequency is incident on it is called photoelectric emission. The electrons, so emitted are called photoelectrons., (iii) Field emission- The emission of electrons from a metal, surface by employing a strong electric field is called field, emission., (iv) Secondary emission-The emission of electrons froma, metal surface when fast moving electrons (called primary, electrons) strike the surface is called secondary emission., The fast moving electrons transfer their energy to the free, , electrons and hence they escape from the surface. These, electrons are called the secondary electrons., , Important characteristics of photon, (i) Energy is emitted by its source in the form of photons, which travel in straight lines with the velocity of light i.e, *3 « 10% m/s in vacuum,, (ii) The photons are packets of energy. The energy (E) of, a photon of frequency (v) is given by, , E=hv, (iii) When a photon passes from one medium to another,, its frequency remains unchanged but its wavelength, , changes. As a result, a photon travels with different velocities in different media., , (iv) Rest mass of a photon is zero and hence it cannot, exist at rest. This can be established from the formula, , m,, , ' Vi - vie", where m, is the rest mass of particle, m is the mass of the, particle moving with velocity v and c is sthe velocity of, light., As a photon moves with a velocity v =c, m, = 0, , (v) The equivalent mass of a photon of frequency v ts, given by, , E=hv=me, c* cA, , hv. _hv_h, , where A is the wavelength of the photon., (vil) The energy of a photon is generally expressed in electron volt (eV) and 1 eV = 1.6 =x 10°" J, $Photoelectric effect, Ques.- Describe the phenomenon of photoelectric effect., Briefly describe the observations of Hertz, Hallwachs and, Lenard., Ans.-The phenomonon of emission of electrons from a, metallic surface when light of suitable frequency (or wavelength) is incident on it is called photoelectric effect. The, electrons so emitted are called photoelectrons., Hertz's observations- Photoelectric effect was discovered, by Hertz in 1887. In his experimental study on the production of electromagnetic waves by means of a spark discharge, Hertz observed that high voltage sparks across, the detector loop were enhanced when the emitter plate, was illuminated by ultraviolet light from an arc lamp., When light falls on a metal surface. some electrons, near the surface absorb enough energy from the incident, light to overcome the attraction of the positive tons in the, material of the surface and escape intu the surrounding, space., Hallwachs and Lenard's observations- The etfect was investigated is detail by german physicist Hallwachs and, Lenard during the years 1886-1902., , Lenard observed that when ultraviolet light was allowed, to fall on the emitter plate of an evacuated glass tube enclosing two electrodes current flows in the circuit. As soon, as the ultraviolet was stopped, the current flow also stopped., These observations indicate that when ultraviolet light fall, on the emitter C, electrons are ejected from it which are, attracted towards the positive collector plate A by the electric feild. The electrons flow through the evacuated glass, tube resulting in the flow of.current in the external circuit, , if : , @, , In 1888, Hallwachs observed that negatively charged, zinc plate connected to an electroscope lost its charges, when it was iluminated by ultraviolet light. Further, the, , Scanned with CamScanner, , Scanned with CamScanner

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* Noli. brian oy, , , , 01, ght KN oO) photo wa, , Erengy om phetow on (rvs trate ft THUEWt ?, , the uncharged zinc plate became positively charged He, en it was illuminated by ultraviolet light. Positive charge, on a positively charged zinc plate was found to be further enhanced when it was illuminated by ultraviolet light., From these observations he concluded that negatively, charged particles were emitted from the zinc plate when, it was illuminated by ultraviolet light., , Experimental study of photoelectric effect, , Ques.- Describe an experimental arrangement to study, photoelectric effect. Explain the effect of (i) intensity of, light on photoelectric current (ii) potential on photoelectric, current (iii) frequency of incident radiation on stopping, potential., , Ans.-In 1900, Lenard and Millikan studied photoelectric, effect experimentally., , Figure shows a simple experimental arrangement used, to study the photoelectric effect. It consists of an evacuated quartz tube which encloses a photo-sensitive plate C, (called cathode) and plate A (called anode). The anode A, can be given a positive or negative potential with respect, to the cathode C with the help of a potential divider. A, voltmeter V is used to measure the potential difference, between the cathode and the anode. The photoelectric current that flows in the circuit can be measured by the, microammeter., , When monochromatic light of suitable frequency is, incident on the cathode (C) through the window W, electrons are emitted from it. The photoelectrons are attracted, by the anode (A) due to its positive potential and constitute photoelectric current. The effect of variation of different factors on photoelecfric emission is as follows, , , , , , , , , (i) 7 of intensity- al a to Sonar the effect of inten, sity of the incident light on photoelectric emission, the anode A is maintained at a definite positive potential w.r.t. to, the cathode. This can be done by adjusting the voltage, from the battery. Now gradually increase the intensity of, the light incident on the cathode and note down the corresponding values of photoelectric current. It is found that, the photoelectric current increases linearly with the intensity of the light. The graph plotted between the intensity of, light and the photoelectric current is a straight line, as shown, , in figure. A, , Lo% I, , (ii) Effect of potential- when the cathode is exposed to the, light of constant frequency and intensity and the positive, potential on the anode is increased gradually. It is observed, that the photoelectric current increases till it attains a maximum value for a certain value of the positive potential and, beyond which it does not increase. This is the saturation, current., , When a negative potential is applied to the anode A, w.r.t. to the cathode and its value is increases gradually. it, is observed that the photoelectric current decreases rapidly till it becomes zero for a certain negative potential of, the anode A. The minimum negative potential given to the, anode at which the photoelectric current reduces to zero., is called the stopping or cut off potential., , The cut-off potential stops the fastest moving photoelectron (i.e. having maximum K.E.) from reaching the, anode A. If V, is the stopping potential then work done by, the retarding potential V,, in stopping the fastest moving, photoelectron will be, From W =qV, or W=evV,, , This work done must be equal to the maximum kinetic, energy of photoelectrons., , Max K.E. of the photoelectrons, , | inv: =eV,, 2) min, , Here, m is the mass of the electron and v_. is the maximum velocity of the photoelectrons. If the experiment is, repeated with light of the same frequency but of higher, intensity, it is found that the saturation current will be more, but the value of the stopping potential will be the same in, both cases. Therefore, it can be concluded that fora given, frequency of the incident light, the stopping potential is, , independent of the intensity of the incident light., L, , 7, L< ft, S “di, Ja=undt I, , , , , , it = ee 1’, , (iii) Effect of NS auency- 4 In order to study the effect of, frequency of the incident light on the photoelectric current, the cathode is exposed with the light of different trequeicies v, and v, (v, > v,) but of the same intensity and, vary the potential on the anode so that the photoelectric, current decrease from their saturation value to zero value, in each case. It is observed that their saturation current ts, same but the value of stopping potential is different. Higher, the frequency of the incident radiation greater ts the value, of stopping potential (i.e. V,.>V,,,)., , J, <q 3, , , , oV/ Vos,, Note 1, From the Sits it can be concluded that, (a) The saturation current is independent of tite frequency, , of the incident tight and depends on the intensity of the, light., , Scanned with CamScanner, , Scanned with CamScanner

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(b) The stopping potential (i.e. the maximum K.E. of the, photoelectrons) depends only on the frequency and is independent of the intensity of the incident light., , Note 2. Ifa graph is plotted between the stopping potential V_ and the frequency of incident light, then the graph, obtained a straight line. This shows that maximum K.E. of, the photoelectrons (i.e. the stopping potential) increases, linearly with the increase in the frequency of the incident, , light., eV, = hv -h,, =hJ -h-+), > \ ay - ne, , gc ers, , , , The graph also shows that there is a certain minimum value, of the frequency of the incident light v, for which the stopping potential (hence the maximum K.E. of the photoelectrons) is zero. It means that the radiation of frequency less, than v, cannot exhibit photoelectric emission. This minimum frequency of the incident light is called the threshold, or cut off frequency for a given cathode. It is independent, of the intensity of the incident light., , Hence, the minimum frequency of the incident light, below which photoefectric emission does not take place is, called the threshold or cut off frequency of that material., Note 2. Graph shows the variations of V, with v for cathode of different metals 1 and 2 _ Different values of, thershold frequencies are due to different values of their, , work function., , , , Laws of photoelectric emission, Ques.- State the laws of photoelectric emission., , Ans.-On the basis of their experimental studies, Lenard, , , , and Millikan gave the following laws regarding photoelec- _, , tric effect, (i) There is no time lag between the incidence of the light, on the metal surface and emission of photoelecrons from, It., , (ii) For the light of a given frequency incident on a metal, surface the number of photoelectrons emitted per second, is directly proportional to the intensity of the incident light., (iii) The maximum kinetic energy of the photoelectrons, cmitted from a given metal surface is independent of the, intensity of the incident light but depends only on the frequency of the incident light. It increases with the increase, in the frequency of the incident light., , ‘the threshold frequency and K. =, , 3, , (iv) There is acertain minimum frequency of the light incident on a given metal surface below which emission of, photoelectrons does not take place. This is called the threshold frequency for the given metal. The threshold frequency, is independent of the intensity of the light., , Failure of wave theory of light to explain_photoelectric effect, , Ques.- Explain why wave theory of light fails to explain, photoelectric effect., , Ans.- The wave theory of light fails to explain the following features of photoelectric effect , (i) According to the wave nature of light the kinetic energy of the emitted electrons should depend upon the intensity of light but in photoelectric effect the kinetic energy of the emitted electrons is independent of the intensity of light., , (ii) According to the wave nature of light the emission of, photoelectrons should take place for all frequencies of light, ( i.e. threshold frequency should not exist ) but in photoelectric effect the photoelectric emission does not take, place below a certain minimum frequency called threshold frequency., , (iii) According to the wave nature of light there should be, time lag between the incidence of light and the emission of, photoelectrons but in photoelectric effect there is instantaneous emission of photoelecrtrons., , Einstein's photoelectric equation (Einstein's theory, , of photo electric effect), Ques.- Explain Einstein's theory of of pret electric ef, fect., OR :, , Ques.- Establish Einstein's photoelectric equation., Ans.- Einstein in1905, explained photoelectric effect on, the basis of Planck's quantum theory. According to this, theory, light (or electromagnatic radiation) consists of pachets of energy called photon or quanta. The energy of a, photon (E) is given by, , E =hv, where h is Planck's constant and its value is 6.62 x 10°, Js and v is the frequency of the light., , Einstein assumed that one photoelectrons is ejected, from the metal surface when one photon of sufficient energy (i.e. suitable frequency) is incident on it. Consider a, photon of frequency v incident on a metal surface. The, energy of the photon is absorbed by one of the free electrons. A part of this energy is used in liberating the electron from the metal surface which is equal to the work, function >, of the metal and the rest imparts maximum, kinetic energy to the ejected photoelectrons. Applying law, of conservation of energy , we get, , ee, , ease, hv=$,+K_. weet), , where hv is the energy of the incident pliotons. 9,, the work function of the metal and , = hv, where vty, I/2 my,> is the, , Scanned with CamScanner, , Scanned with CamScanner

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maximum kinetic energy of the photoelectrons. Hence, from equation (i), , hv =hv + K, , man, , or KK o=h(v-v) --(ii), This eqution ts called Einstein's photoelectric equation., Note -Millikan experimentallly tested Einstein's equation i, and found that it was consistent with the experimental study, of photoelectric effect., According to Einstein's equation, we have, , E, = hv - hv, (But E,. “¢¥,), eV, = hv - hv,, , vO, , In equation (iii), h and e are constant and v, is constant, for a given metal surface. Hence it is clear that the graph, between the stopping potential (V,) and the frequency of, the light (v) must be a straight line., , , , Fig. shows that the slope of the straight line graph, is Aand its intercept on the potential axis is —Yillikan, measured the slope of the straight line and using the known, value of e calculated the value of h. He found that the, calculated value of h was very close to that obtained by, other methods. Hence the validity of Einstein's equation, was established., , Matter wave-wave nature of particle, , Ques.- What do you mean by dual nature of matter?, Ans.- In 1924 de-Broglie put forward a hypothesis that, like radiation, matter should also possess dual nature. According to him a moving material particle sometimes acts, as a wave and sometimes as a particle i.e. a wave is associated with a moving material particle. His hypothesis was, based on the following facts, (a) The whole energy in the universe is in the form of, radiation and matter. Hence both these forms should possess similar characteristics., , (b) There is symmetry in nature. Hence if radiation has, dual nature, matter must also possess dual nature., , The wave associated with moving particle i.e. matter is called matter wave or deBroglie wave. The wavelength of de-Broglie wave of a particle called de-Broglie, wave length and is given by, , r= JL, mv, where m and v are the mass and velocity of the particle, , and h is Planck's constant., , Expression for de-Broglie’s wavelength (deBroglie's wave equation), , Ques.- Derive de-Broglie's wave equation for material, particles., , Ans.-According to Planck's quantum theory, the energy, (E) of a photon of a radiation of frequency (v) is given by, , , , 4, E=hv, If the photon is considered as a particle of mass m then, according to Einstein's mass energy relation., E = me, Since energy of the photon in the two cases is same hence, hv = me, Vv h, , me =h = 2 (From c = vi), , But mc is the momentum of the photon of mass m and, travelling with the velocity of light c, _h, , r, , h, or = a—_, P, , de-Broglie suggested that equation is general formula and, stands valid both for the photon as well as for the other, moving material particles. Hence, if a particle of mass m, is moving with a velocity v .the wavelength of the matter, wave associated with it is given by., h h, , = — Tie, This is de-Broglie's wave equation for material particles., It relates a characteristics of the wave (i.e. wavelength), to a characteristic of the particle (i.e. mass)., From this equation, it can be concluded that, (i) If v=0, then A = 00, Hence matter waves are associated with the material particle only when they are in motion., (ii) de-Broglie's waves are associated with material particles wheather they are charged or not charged., (111) de-Broglie’s waves cannot be electromagnetic in nature because electromagnetic waves are only associated, with accelerated charged particles., Note-A schematic diagram of a matter wave is given in, fig., , , , De-Broglie wavelength of an electron, , Ques.- Deduce an expression for the de Broglie wavelength of an electron accelerated through a potential ditference of V volts., , Ans.- Consider an electron mass m and charge e accelerated through a potential difference of V volts. Then kinetic energy acquired by the electron, , | __s, E= smv= eV (From WV =qV ), y= eV, m, de-Broglie wavelength associated with the electron, h h ——, r = = . = WmE, ("os y 2mE, (From p = V2mE, ), or A= wth, ¢ V2meV, Substituting the values of h, m and e in the above equation, we get i, i = 6.6310, , = N23 9.1 ® 10" * 1.6% 10 '¥, , Scanned with CamScanner, , Scanned with CamScanner

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a, , In ae ifa eatite of charge (q) and mass (1m) is accelerated through a potential difference of V volts, then, de-Broglie wave of the particle is {, , 1 = p=, p=, , Davisson and Germer experiment, Ques.- Describe Davisson and Germer experiment to, demonstrate the wave nature of electrons., Ans.- In 1927, Davisson and Germer gave the first ex, perimental demonstration of the wave nature of slow moving electrons., , The apparatus used i by them is shown in fig., , fle, , OT, , , , , , It consists of an electron, gun which is made of a, filament (F), a tungsten cathode (C) coated with barium, oxide and acylindrical anode (A) with a small hole. When, the filament is heated by passing the current through it, using a low tension battery(L.T.), the cathode gets heated, indirectly and large number of electrons are emitted from, the cathode. These electrons are accelerated through a, variable potential difference V applied between the cathode and the anode. The narrow hole in the anode confines, , the diverging elecirons into a fine beam. This fine beam of, , low energy electrons is allowed to fall normally on a nickel, crystal (N) and the intensity of the electrons (i.e number, of electrons) scattered by the atoms of the crystal can be, in measured with the help of a detector. The detector can, be rotated along a circular scale (S) centred at O to measure the intensity of the scattered electrons in different directions. Graphs are plotted between the scattering angles (>) and the intensity (I) of the scattered beam for, different accelerating potentials (V)., , Dinekorr 04, , , , , id, 0 Ae Sav, It is clear from these graphs that, (i) The intensity of scattered electrons depends upon the, angle of scattering (6)., , (ii) There is a bump of bend in each curve at 6 = 50°. The, size of bump increases with the increase of accelerating, , ), potential and it becomes maximum when accelerating potential becomes 54 V. On further increasing the accelerating potential the size of bump decreases., , (iii) The maximum size of bump i.e. the sharp peak at, $ = 50° and V = 54 volts is due to the constructive interference between the electron beams scattered from various atoms of the crystal i.e. strong diffraction of electron, beam at the crystal occurs at 54 volts at 50°.Since phenomenon of diffraction is exhibited by waves therefore, electron beam exhibits the wave character in Davisson, and Germer experiment ., From fig., , 6+6+6 = 180°, , or 20=180°-6, = 180° - 50°, , @ = 65°, For Ni crystal, the interatomic distance d = 0.91 A, Now according to Bragg's law, the nth diffraction maximum is given by, , 2dsin@ =nA, , For first order diffraction n= |, . 2dsinO=A, or A= 20.91 x 10" x sin 65°, or A=1.66A, mune V = 54V in ean, , _ 2227, , ~ WV, , 1227., or A= ‘sq, or A=1.67A, , As the two results are in agreement with one another therefore the wave nature “of electron and hence the de-Broglie, hypothesis is confirmed., , Scanned with CamScanner, , Scanned with CamScanner