Dual Nature of matter and radiation: m v 1 c

Transcription

1 Dual Nature of matter and radiation: Potons: Electromagnetic radiation travels in space in te form discrete packets of energy called potons. Tese potons travel in straigt line wit te speed of ligt. Important Properties of potons: [1] According to quantum teory of ligt, radiation from any given source always travel in te form of potons. []Potons always travel along te straigt-line pat. [3] Te energy of poton is given by c E = Were is Planck s constant and its value is 6.6x10-34 Js [4] Velocity of poton is equal to te velocity of ligt i.e. 3 x 10 8 m/s [5] Te mass of te particle varies wit velocity according to te relation m= m 0 v 1 c were m 0 denotes rest mass of te particle. As poton moves wit te velocity of ligt v=c, tus m 0 =0. Hence poton as zero rest mass. Te equivalent mass of te poton is given by using relation m= [6] Momentum of poton is given by relation p=mc= c [7] Potons are electrically neutral particle and tey are not deflected by te eiter electric or magnetic field. [8] Te velocity of potons in different media is different due to te cange in wavelengt, but te frequency of poton remains constant. Free electrons in metals: In metals, te electrons in te outermost sell of te atoms are loosely bound. It is because of te small attractive force between te positive nucleus and electrons in te outermost sell. Tese electrons can freely move in a metal like gas molecules in a given volume of certain gas. But te electron can t leave te metal surface because of te attractive force of oter positive carges. Tere exist a potential barrier wic tey must overcome before leaving te surface. To overcome tat potential barrier tey require certain minimum amount of energy. Tis minimum energy required by an electron just to escape from te metal surface so as to overcome te restraining forces is called work function. Work function is generally denoted by 0. c Electron Emission: Electron emission is defined as te penomenon of emission of free electrons from te metal surface. Te various modes for providing energy to te electrons and making tem free are [a] Termionic emission: It is penomenon of emission of free electrons from te metal surface wen eated suitably. On eating te metal, te free electrons acquire sufficient energy to overcome te restraining forces. Te electrons so emitted are called termal electrons or termions. Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

2 [b] Potoelectric emission; It is te penomenon of emission of electrons from te metal surface wen ligt of suitable energy falls on tem. By suitable energy we mean tat te energy of incident potons sould be more tan te work function from te metal surface. Te emitted electrons are potoelectrons. [c] Field emission: Te penomenon of emission of electrons from te metal surface wen strong electric field is applied across it. Te electric field intensity will provide energy to te electrons and te emitted electrons are field electrons. Electric field of te order of 10 8 V/m is required for emission. [d] Secondary emission; Wen fast moving electrons called primary electrons are allowed to fall on te metal surface, tey collide wit te free electrons inside te metal surface. Te energy transfer between primary electrons and electrons inside te metal surface provides electron emission from te metal surface. Te emitted electrons are called secondary electrons. Potoelectric effect: Te penomenon of emission of electrons from te metal surface wen radiation of suitable frequency falls on tem is called potoelectric effect. Te emitted electrons are called potoelectrons and te corresponding current is called potoelectric current. Te suitable energy [work function] for different metals is different. Alkali metals can emit electrons even wit visible ligt wereas metals like zinc or magnesium requires ultraviolet ligt. Effect of intensity; If we consider tree different poton beams striking te metal surface aving same frequency but different intensity [I 1 >I >I 3 ], ten te potoelectric current will be different in te 3 cases. Larger te intensity larger will be te potoelectric current as sown in te grap. But because te frequency of incident beam is same sopping potential for all te tree beams will be equal. Effect of potential: Wen we increase te potential of A w.r.t. Catode, for a given value of intensity and frequency it was found tat te potoelectric current also increases. At one particular value of accelerating voltage te grap becomes orizontal or te potoelectric current saturates. If we increase te Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

3 potential beyond tis value te current will remain constant. Tis basically implies tat all te electrons emitted by te catode ad started reacing te plate A. If negative potential is applied on A relative to C, te potoelectric current decreases as electrons emitted by te catode are repelled by te negative potential of plate C. tus, lesser number of electrons will be able to reac te plate A. It was found te potoelectric current tan decreases rapidly till it reduces to zero at certain negative value of potential of plate A relative to B. Tis, minimum negative potential V 0, of plate A relative to B for wic te potoelectric current becomes zero is called stopping potential. If e denotes te carge on electron, ten 1 ev 0 = mv max Te following grap indicates tat for different intensities but te same frequency, te potoelectric current is different but as te frequency and tus maximum kinetic energy is same tus stopping potential will also be same in all te tree cases. Effect Of Frequency: If we take 3 radiations of different frequency but aving te same intensity. In tis case, te number of potons striking te metal surface per second per unit area will be same, tus, te potoelectric current will be same in all te tree cases. But, as te frequency of poton beams is different te maximum kinetic energy of emitted potons will also be different. Larger te frequency of incident poton beam larger will be te maximum kinetic energy and larger will be te magnitude of te stopping potential. Variation of stopping potential wit frequency: Te stopping potential varies linearly wit te frequency of incident poton beam. If frequency of poton beam is less tan te tresold frequency ten te stopping potential will be zero as no potoelectric current flows. But if > 0, stopping potential increases wit. Laws of potoelectric emission: [a] For a given metal surface and frequency of te incident radiation, te number of potoelectrons ejected per second by te metal surface is directly proportional to te intensity of te incident ligt. [] For a given metal surface, tere exists a minimum frequency of incident radiation below wic no emission of electrons will take place. Tis frequency is called tresold frequency. [3] Above te tresold frequency, te maximum kinetic energy of emitted potoelectrons is independent of te intensity of incident radiation and depends only on te frequency of te incident radiation. Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

4 [4] Te potoelectric effect is in instantaneous penomenon. Te time lag between te poton striking te metal surface and emission of electrons is only 10-9 s Einstein s Potoelectric Equation; Einstein explained te laws of potoelectric effect using Planck s quantum teory of ligt. It states tat ligt consists of tiny packets of energy called quanta. One quantum of ligt radiation is called poton wic travels wit te speed of ligt and wose energy is given by E = Einstein assumed tat one potoelectron will be emitted by te metal surface wen one of suitable energy falls on it. Wen poton of energy is incident on te metal surface its energy will be used in parts [a] A part of energy is used in liberating te electron from te metal surface wic is equal to work function for te given metal [] te ret of energy is given to te poton in te form of its kinetic energy. Tus, for a poton of energy te energy equation can be written as = mv 1 mv = - 0 Tis equation is known as Einstein s potoelectric equation. If 0 denotes te work function or tresold energy of te metal surface ten te corresponding tresold frequency is given by 0. 1 mv = mv = c 0 ere 0 and signifies te tresold wavelengt and wavelengt of te incident poton respectively. Explanation of laws of potoelectric effect: [1] According to Einstein s assumption, one poton is completely absorbed by te electron for its emission from te metal surface. Tus number of electrons ejected per second per unit area can t be more tan te number of potons incident on te surface per second per unit area. Hence potoelectric current depends upon te intensity of incident poton beam. [] If frequency of incident poton beam is less tan te tresold frequency i.e. < 0, ten te kinetic energy of emitted electrons will be negative and te velocity comes out be imaginary wic is never possible. Tus, emission of electrons from te metal surface can take place only if te frequency of incident poton beam is more tan te tresold frequency of te metal surface. [3]As 0 for any given metal surface is constant, it implies tat te kinetic energy of emitted electrons depends only on te frequency of te incident radiation falling on te metal surface and is independent of te intensity of te incident poton beam. [4] Wen poton falls on te metal surface immediately an electron is ejected by te metal surface if te frequency of te incident beam is more tan te tresold frequency. Tus it is an instantaneous penomenon. Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

5 [5]Wen te supply of potons is cut off, te emission of te potoelectrons also stops from te metal surface. Also as te Einstein s equation doesn t involve temperature, we can conclude tat te potoelectric emission is independent of te temperature of te catode. Relation between Stopping potential, frequency of incident poton beam and tresold frequency; According to Einstein s potoelectric equation te maximum kinetic energy of emitted potoelectrons is difference of incident energy and tresold energy. E max = - 0 If V 0 is te cut off potential, as te electrons stops in te pat its initial kinetic energy gets converted into final potential energy. ev 0 = E max ev 0 = ( - 0 ) ev 0 = c Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar # c were is te wavelengt of te incident poton beam and 0 is te tresold wavelengt for te metal surface. Potoelectric Cell: It is a device wic converts ligt energy into te electrical energy. Potoelectric cells can be 3 types [a] Poto emissive Cell; Potoemissive cell or pototube as it is commonly called consists of galls or quartz tube wit semi cylindrical metal plate acting as catode and wire loop acting as anode. Te tube as insulating base wit metallic pins to fix te tube in te socket. Tis tube is connected to te external circuit using battery and micro ammeter and a load resistance R. Wen ligt of frequency greater tan te tresold frequency for te metal surface is allowed to fall on te catode, potoelectrons are emitted. Tese are attracted by te positive potential on te anode loop and current begins to flow in te circuit. Te potoelectric current, wic flows in te circuit, is measured using microammeter. Tis current is generally very small and needs amplification before it can be used. Te current flows only till te potons are falling on te metal surface. [b] Potovoltaic Cell: It consists of tree layers as sown in figure. Te metallic surface of copper or gold wit tin semi conducting layer of cuprous oxide and a tin transparent film of silver or gold. Wen sunligt falls on te top transparent layer and passes troug it, it illuminates te semiconducting layer. Te potoelectrons are emitted by tis layer and are collected by top layer. Tis cerates a potential difference between te top two layers and conventional current begins to flow. Tus, cell supplies current witout any batteries. Here also, te potoelectric current is directly proportional to te intensity of te incident ligt falling on te surface. [c] Potoconductive cell: Potoconductive cell as its working based on te principle tat te

6 electrical resistance of te semi conductors decreases wit te increase in temperature of te semiconductor. It consists of tin transparent surface film wic is placed on tin layer of selenium [semi conductor] wic in turn is placed on iron layer. A potential difference is applied across te surface of te film and iron layer. Wen ligt os suitable frequency falls on te surface fim, electrical resistance of te semiconductor decreases and current begins to flow in te outer circuit, tis current canges wit te cange in intensity of te incident ligt. Applications of Potoelectric Cells; [a] It is used as burglar alarm in ouses or banks etc. [] A potocell can be used to locate flaws in te metallic seet in industrial applications [3] It is used for automatic switcing on and off of te streetligts. [4] It is used for automatic counting of number of persons entering or leaving a given all or stadium. [5] It is used as fire alarm in te case of accidental fire in te building [6]potoelectric cells are used in TV and camera for telecasting scenes by converting ligt and sade into electric signals. [7] Potocells are used to compare te illuminating power of two different sources of ligt. Dual Nature of matter; Tere are some penomenon involving ligt like potoelectric effect, Compton scattering etc wic can be explained only if we assume te ligt to possess te particle caracter. Wereas, some oter penomenon like diffraction etc can be explained by assuming te ligt to be possessing wave caracter. Tis implies tat ligt posses bot particle as well as wave caracter. Tus, ligt penomenon can be classified into 3 categories [1] te penomenon like potoelectric effect or Compton scattering wic can be explained using particle caracter [] Te penomenon like diffraction or polarization, wic can be, explained only using wave caracter. [3] Penomenon like refraction or refraction, wic are based on rectilinear propagation, wic can be, explained eiter by particle or wave caracter. De-Broglie Hypotesis {Matter Waves} De-Broglie stated tat as ligt posses dual caracter and universe consists of matter and radiation only. As nature loves symmetry, tus matter sould also possess dual nature bot particle as well as a wave. According to de-broglie a wave is always associated wit te moving particle wic controls te particle in every aspect. Tis wave is called de-broglie wave or matter wave. For a particle of mass m moving wit te velocity v te de-broglie wavelengt associated wit te particle is given by Proof;` According to Planck s quantum teory, te energy associated wit a potn of frequency is given by E = Also, according to relativistic mass formula for particle of rest mass m 0 and momentum p te energy is given by E = Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar # mv p c As rest mass of te poton is zero, tus energy of poton beam is given by m 0 c 4

7 E = pc Equating te two values of energy = pc p = c = p De- Broglie stated tat as potons and matter particles beaves in similar manner, tere te same formula can be applied to matter particle also, wose momentum is equal to mv. Tus, = mv Tus, if te velocity of te particle is zero, its wavelengt will be infinity and if velocity of te particle is infinity te wavelengt will be zero. In daily life te mass of te particle and tus tere momentum is very large. Te de-broglie wavelengt tus, comes out to be small. Te de-broglie wavelengt of any particle is independent of te carge on te particle. Note: It was found tat velocity of De-Broglie waves is always more tan te velocity wit wic te particle moves. De-Broglie Wavelengt of te electron; If an electron is made to accelerate troug te potential difference of V volt, te initial electrical potential energy of te electron gets converted into final kinetic energy of te electron 1 ev= mv p ev= m p= mev Tus, according to De-Broglie s relation, te corresponding wavelengt associated wit te electron is = p mev As,,m and e are constant, if we substitute teir values we get = A V Davisson And Germer experiment: Davisson and Germer experiment was performed to proof te dual nature of electrons [matter]. Experimental setup used by tem is as sown in figure. Te process of Termionic emission emits te electrons from te tungsten Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

8 catode. Tese electrons are accelerated by a potential difference of V volt between catode and anode A. A narrow ole in te anode renders electrons into a fine beam of electrons, wic is made to strike te nickel crystal. Te electrons are scattered in different directions and te intensity of scattered electrons in different directions is measured using a detector. Te intensity is measured for different values of wic is angle between te direction of incident ligt and scattered direction of electron beam. Te grap is plotted between and intensity for different values of accelerating voltages. Following conclusions can be drawn from te grap [a] Intensity of scatted beam depends upon te angle of scattering. [b] Tere is always a bump or kink signifying large intensity at =50 0 [c] Te size of te bump canges wit te accelerating voltage and is maximum wen accelerating voltage becomes 54V [d] Te size of bump decreases if we furter increase te accelerating voltage. Te selective reflection of te 54V electron at an angle of 50 0 between te incident and scattered beam can be termed as diffraction of electrons from te regularly spaced electrons of nickel crystal by virtue of teir wave nature. 1 = 180 = 65 0 According Bragg s diffraction equation, for first order maxima[n=1] d sin = For nickel crystal te distance between atomic planes is 0.91A = x 0.91 x sin 65 = 1.66A if we assume te electron to be a particle wic sows maxima wen te accelerating voltage is 54V, ten 1.7 = 1.65A 54 As, bot te result assuming electron to be particle and wave are identical we conclude tat te electrons possess dual caracter. Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #

9 Residence: 86, Cotti Baradari Part 1,[Near Medical College], Gara Road, Jalandar #