High potential difference + Gas. Manometer. Vacuum pump

Transcription

1 Lig genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays + lectric Discarge Troug Gases. At noral atosperic pressure, te gases are poor conductor of electricity. If we establis a potential difference (of te order of 30 kv) between two electrodes placed in air at a distance of few c fro eac oter, electric conduction starts in te for of sparks. Te passage of electric current troug air is called electric discarge troug te air. Te discarge of electricity troug gases can be systeatically studied wit te elp of discarge tube sown below Hig potential difference + Gas Lengt of discarge tube 30 to 40 c Diaeter of te tube 4c Manoeter Te discarge tube is filled wit te gas troug wic discarge is to be studied. Te pressure of te enclosed gas can be reduced wit te elp of a vacuu pup and it's value is read by anoeter. Sequence of penoenon Vacuu pup As te pressure inside te discarge tube is gradually reduced, te following is te sequence of penoenon tat are observed. Streaers + Positive + colun Negative glow Positive colun + 0 of Hg Below 4 of Hg F.D.S..5 of Hg Negative glow Positive colun + Catode glow Negative glow + Catode glow C.D.S. F.D.S. 0.8 of Hg C.D.S. () At noral pressure no discarge takes place. F.D.S. Striations 0.05 of Hg 0.0 of Hg Greenis ligt () At te pressure 0 of Hg, a zig-zag tin red spark runs fro one electrode to oter and cracking sound is eard. (3) At te pressure 4. of Hg, an illuination is observed at te electrodes and te rest of te tube appears dark. Tis type of discarge is called dark discarge. (4) Wen te pressure falls below 4 of Hg ten te wole tube is filled wit brigt ligt called positive colun and colour of ligt depends upon te nature of gas in te tube as sown in te following table. Gas Air Colour Purple red

2 lectron, Poton, Potoelectric ffect and X-rays H N Cl CO Na Neon Blue Red Green Bluis wite Yellow Dark red (5) At a pressure of.5 of Hg : (i) Sky colour ligt is produced at te catode it is called as negative glow. (ii) Positive colun srinks towards te anode and te dark space between positive colun and negative glow is called Faradays dark space (FDS) () At a pressure of 0.8 Hg : At tis pressure, negative glow is detaced fro te catode and oves towards te anode. Te dark space created between catode and negative glow is called as Crook's dark space lengt of positive colun furter reduced. A glow appear at catode called catode glow. (7) At a pressure of 0.05 of Hg : Te positive colun splits into dark and brigt disc of ligt called striations. (8) At te pressure of 0.0 or 0 of Hg soe invisible particle ove fro catode wic on striking wit te glass tube of te opposite side of catode cause te tube to glow. Tese invisible rays eerging fro catode are called catode rays. (9) Finally wen pressure drops to nearly 0 4 of Hg, tere is no discarge in tube. Catode Rays. Catode rays, discovered by sir Williu Crooke are te strea of electrons. Tey can be produced by using a discarge tube containing gas at a low pressure of te order of 0 of Hg. At tis pressure te gas olecules ionise and te eitted electrons travel towards positive potential of anode. Te positive ions it te catode to cause eission of electrons fro catode. Tese electrons also ove towards anode. Tus te catode rays in te discarge tube are te electrons produced due to ionisation of gas and tat eitted by catode due to collision of positive ions. () Properties of catode rays (i) Catode rays travel in straigt lines (cast sadows of objects placed in teir pat) (ii) Catode rays eit norally fro te catode surface. Teir direction is independent of te position of te anode. (iii) Catode rays exert ecanical force on te objects tey strike. (iv) Catode rays produce eat wen tey strikes a aterial surface. (v) Catode rays produce fluorescence. (vi) Wen catode rays strike a solid object, specially a etal of ig atoic weigt and ig elting point X-rays are eitted fro te objects. (vii) Catode rays are deflected by an electric field and also by a agnetic field. (viii) Catode rays ionise te gases troug wic tey are passed. (ix) Catode rays can penetrate troug tin foils of etal. (x) Catode rays are found to ave velocity ranging t to t of velocity of ligt () J.J. Toson's etod to deterine specific carge of electron

3 lectron, Poton, Potoelectric ffect and X-rays 3 It's working is based on te fact tat if a bea of electron is subjected to te crossed electric field and agnetic field B, it experiences a force due to eac field. In case te forces on te electrons in te electron bea due to tese fields are equal and opposite, te bea reains undeflected. C = Catode, A = Anode, F = Filaent, LT = Battery to eat te filaent, V = potential difference to accelerate te electrons, SS' = ZnS coated screen, XY = etallic plates (lectric field produced between te) (i) Wen no field is applied, te electron bea produces illuinations at point P. (ii) In te presence of any field (electric and agnetic) electron bea deflected up or down (illuination at P ' or P '') (iii) If bot te fields are applied siultaneously and adjusted suc tat electron bea passes undeflected and produces illuination at point P. In tis case; lectric force = Magnetic force e = evb v ; v = velocity of electron B As electron bea accelerated fro catode to anode its potential energy at te catode appears as gain in te K.. at te anode. If suppose V is te potential difference between catode and anode ten, potential energy = ev And gain in kinetic energy at anode will be K.. e Toson found,.77 0 C / kg. Note : Positive Rays. L.T. v i.e. ev v e v V e l Te deflection of an electron in a purely electric field is given by y. ; were l v lengt of eac plate, y = deflection of electron in te field region, v = speed of te electron. Positive rays are soeties known as te canal rays. Tese were discovered by Goldstein. If te catode of a discarge tube as oles in it and te pressure of te gas is around 0 3 of Hg ten faint luinous glow coes out fro eac ole on te backside of te catode. It is said positive rays wic are coing out fro te oles. C (H.T.) + e A l X Y y + Magnetic field S S P P P e VB Positive rays () Origin of positive rays Wen potential difference is applied across te electrodes, electrons are eitted fro te catode. As tey ove towards anode, tey gain energy. Tese energetic electrons wen collide wit te atos of te gas in te discarge tube, tey ionize te atos. Te positive ions so fored at various places between catode and anode, travel towards te catode. Since during teir otion, te positive ions wen reac te catode, soe pass troug te oles in te catode. Tese streas are te positive rays. () Properties of positive rays

4 4 lectron, Poton, Potoelectric ffect and X-rays (i) Tese are positive ions aving sae ass if te experiental gas does not ave isotopes. However if te gas as isotopes ten positive rays are group of positive ions aving different asses. (ii) Tey travels in straigt lines and cast sadows of objects placed in teir pat. But te speed of te positive rays is uc saller tan tat of catode rays. (iii) Tey are deflected by electric and agnetic fields but te deflections are sall as copared to tat for catode rays. (iv) Tey sow a spectru of velocities. Different positive ions ove wit different velocities. Being eavy, teir velocity is uc less tan tat of catode rays. (v) q / ratio of tese rays depends on te nature of te gas in te tube (wile in case of te catode rays q/ is constant and doesn't depend on te gas in te tube). q/ for ydrogen is axiu. (vi) Tey carry energy and oentu. Te kinetic energy of positive rays is ore tan tat of catode rays. (vii) Te value of carge on positive rays is an integral ultiple of electronic carge. (viii) Tey cause ionisation (wic is uc ore tan tat produced by catode rays). Mass Spectrograp. It is a device used to deterine te ass or (q/) of positive ions. () Toson ass spectrograp It is used to easure atoic asses of various isotopes in gas. Tis is done by easuring q/ of singly ionised positive ions of te gas. Low pressure gas Te positive ions are produced N in te bulb at te left and side. Tese ions are accelerated towards N catode. Soe of Pup te positive ions pass troug te fine ole in te catode. Tis fine ray of positive ions is D subjected to electric field and agnetic field B and ten allowed to strike a fluorescent screen ( B but or B v ). If te initial otion of te ions is in x direction and electric and agnetic fields are applied along y axis ten force due to electric field is in te direction of y-axis and due to agnetic field it is along z-direction. qld Te deflection due to electric field alone y...(i) v qbld Te deflection due to agnetic field alone z...(ii) v Fro equation (i) and (ii) q B LD z k y, were k ; Tis is te equation of parabola. It eans all te carged particles oving wit different velocities but of sae q/ value will strike te screen placed in yz plane on a parabolic track as sown in te above figure. Note : Catode All te positive ions of sae. q/ oving wit different velocity lie on te sae parabola. Higer is te velocity lower is te value of y and z. Te ions of different specific carge will lie on different parabola. Y P Q S V3 V4 V V + V>V>V3>V4 Z Screen or Poto plate Ligt ass Heavy ass +q v S q/ q/ large sall q/ q/ sall large y Y z Z Te nuber of parabola tells te nuber of isotopes present in te given ionic bea. () Bainbridge ass spectrograp

5 lectron, Poton, Potoelectric ffect and X-rays 5 In Bainbridge ass spectrograp, field particles of sae velocity are selected by using a velocity selector and ten tey are subjected to a unifor agnetic field perpendicular to te velocity of te particles. Te particles corresponding to different isotopes follow different circular pats as sown in te figure. (i) Velocity selector : Te positive ions aving a certain velocity v gets isolated fro all oter velocity particles. In tis caber te electric and agnetic fields are so balanced tat te particle oves undeflected. For tis te necessary condition is v. B (ii) Analysing caber : In tis caber agnetic field B is applied perpendicular to te direction of otion of te particle. As a result te particles ove along a circular pat of radius q r r also qbb ' BB ' r r In tis way te particles of different asses gets deflected on circles of different radii and reac on different points on te poto plate. Note : Separation between two traces v( ) d r r d. qb' Matter waves (de-broglie Waves). According to de-broglie a oving aterial particle soeties acts as a wave and soeties as a particle. or A wave is associated wit oving aterial particle wic control te particle in every respect. Te wave associated wit oving particle is called atter wave or de-broglie wave and it propagates in te for of wave packets wit group velocity. +q v Velocity spectru B Potograpic plate r r r B () de-broglie wavelengt According to de-broglie teory, te wavelengt of de-broglie wave is given by p v p v Were = Plank's constant, = Mass of te particle, v = Speed of te particle, = nergy of te particle. Te sallest wavelengt wose easureent is possible is tat of -rays. Te wavelengt of atter waves associated wit te icroscopic particles like electron, proton, 0 neutron, -particle etc. is of te order of 0. (i) de-broglie wavelengt associated wit te carged particles. Te energy of a carged particle accelerated troug potential difference V is Hence de-broglie wavelengt p qv electron Å, proton Å, deutron Å, V V V (ii) de-broglie wavelengt associated wit uncarged particles. For Neutron de-broglie wavelengt is given as Neutron nergy of teral neutrons at ordinary teperature (in ev) 0 particle v 0.8 Å (in ev ) qv 0.0 Å V

6 lectron, Poton, Potoelectric ffect and X-rays kt kt ; were k = Boltzan's constant = tep. So Teral Neutron Å T T Joules/kelvin, T = Absolute () Soe graps p Slope = /b Sall Large v Note : Sall Large / V Sall Large A poton is not a aterial particle. It is a quanta of energy. Wen a particle exibits wave nature, it is associated wit a wave packet, rater ten a wave. (3) Caracteristics of atter waves (i) Matter wave represents te probability of finding a particle in space. (ii) Matter waves are not electroagnetic in nature. (iii) de-brogile or atter wave is independent of te carge on te aterial particle. It eans, atter wave of de-broglie wave is associated wit every oving particle (weter carged or uncarged). (iv) Practical observation of atter waves is possible only wen te de-broglie wavelengt is of te order of te size of te particles is nature. (v) lectron icroscope works on te basis of de-broglie waves. (vi) Te electric carge as no effect on te atter waves or teir wavelengt. (vii) Te pase velocity of te atter waves can be greater tan te speed of te ligt. (viii) Matter waves can propagate in vacuu, ence tey are not ecanical waves. (ix) Te nuber of de-broglie waves associated wit n t orbital electron is n. (x) Only tose circular orbits around te nucleus are stable wose circuference is integral ultiple of de-broglie wavelengt associated wit te orbital electron. (4) Davision and Gerer experient It is used to study te scattering of electron fro a solid or to verify te wave nature of electron. A bea of electrons eitted by electron gun is ade to fall on nickel crystal cut along cubical axis at a particular angle. Ni crystal beaves like a tree diensional diffraction grating and it diffracts te electron bea obtained fro electron gun. Sall Large Incident bea of electrons F lectron gun Detector Diffracted bea of electrons Te diffracted bea of electrons is received by te detector wic can be positioned at any angle by Nickel crystal rotating it about te point of incidence. Te energy of te incident bea of electrons can also be varied by canging te applied voltage to te electron gun.

7 Incident bea Incident bea Incident bea Incident bea genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays 7 According to classical pysics, te intensity of scattered bea of electrons at all scattering angle will be sae but Davisson and Gerer, found tat te intensity of scattered bea of electrons was not te sae but different at different angles of scattering. forula Intensity is axiu at 54 V potential difference and 50 o diffraction angle. If te de-broglie waves exist for electrons ten tese sould be diffracted as X-rays. Using te Bragg's d sin n, we can deterine te wavelengt of tese waves. ( 80 ) Were d = distance between diffracting planes, = glancing angle for incident bea = Bragg's angle. Te distance between diffraction planes in Ni-crystal for tis experient is d = 0.9Å and te Bragg's angle = 5 o. Tis gives for n =, sin 5 o.5 Å.7.7 Now te de-broglie wavelengt can also be deterined by using te forula.7 Å. V 54 Tus te de-broglie ypotesis is verified. Heisenberg Uncertainty Principle. According to Heisenberg's uncertainty principle, it is ipossible to easure siultaneously bot te position and te oentu of te particle. Let x and p be te uncertainty in te siultaneous easureent of te position and oentu of te particle, ten x p ; were If x = 0 ten p = and = J-s is te Planck's constant. and if p = 0 ten x = i.e., if we are able to easure te exact position of te particle (say an electron) ten te uncertainty in te easureent of te linear oentu of te particle is infinite. Siilarly, if we are able to easure te exact linear oentu of te particle i.e., p = 0, ten we can not easure te exact position of te particle at tat tie. Poton. 44 V According to ienstein's quantu teory ligt propagates in te bundles (packets or quanta) of energy, eac bundle being called a poton and possessing energy. () nergy of poton c nergy of eac poton is given by ; were c = Speed of ligt, = Plank's constant = J- sec, = Frequency in Hz, = Wavelengt of ligt c 375 nergy of poton in electron volt ( ev ) e ( Å) 400 ( Å) () Mass of poton Actually rest ass of te poton is zero. But it's effective ass is given as c. Tis ass is also known as kinetic ass of te poton c c c (3) Moentu of te poton Moentu p c c 48 V c 50 o 54 V =5 D 4 V d =50 Atoic planes

8 8 lectron, Poton, Potoelectric ffect and X-rays (4) Nuber of eitted potons Te nuber of potons eitted per second fro a source of onocroatic radiation of wavelengt P P P and power P is given as ( n ) ; were = energy of eac poton c (5) Intensity of ligt (I) nergy crossing per unit area norally per second is called intensity or energy flux P i.e. I P radiation power At A t P At a distance r fro a point source of power P intensity is given by I I 4r r Concepts Discovery of positive rays elps in discovering of isotopes. Te de-broglie wavelengt of electrons in first Bor orbit of an ato is equal to circuference of orbit. A particle aving zero rest ass and non zero energy and oentu ust travels wit a speed equal to speed of ligt. de-broglie wave lengt associates wit gas olecules is given as (nergy of gas olecules v kt at teperature T is 3 kt ) rs 3 xaple: Te ratio of specific carge of an -particle to tat of a proton is [BCC 003] (a) : (b) : (c) : (d) : 3 q ( q / ) q p Specific carge ; Ratio. ( q / ) q p p 0 xaple: Te speed of an electron aving a wavelengt of 0 is [AIIMS 00] (a) /s (b). 0 / s (c) / s (d) / s Solution : (a) xaple: 3 xaple: By using electron v / s. 3 0 ev ee In Toson experient of finding e/ for electrons, bea of electron is replaced by tat of uons (particle wit sae carge as of electrons but ass 08 ties tat of electrons). No deflection condition in tis case satisfied if [Orissa (ngg.) 00] (a) B is increased 08 ties (b) is increased 08 ties (c) B is increased 4.4 ties (d) None of tese In te condition of no deflection e VB. If is increased to 08 ties ten B sould be increased by ties. In a Toson set-up for te deterination of e/, electrons accelerated by.5 kv enter te region of 4 crossed electric and agnetic fields of strengts 3. 0 V and. 0 3 T respectively and go troug undeflected. Te easured value of e/ of te electron is equal to [AMU 00] (a).0 0 C-kg - (b).7 0 C-kg - (c).80 0 C-kg - (d).85 0 C-kg - By using e ( 3. 0 )..8 0 C / kg 3 3 VB.5 0 (. 0 ) xaple: 5 In Bainbridge ass spectrograp a potential difference of 000 V is applied between two plates distant c apart and agnetic field in B = T. Te velocity of undeflected positive ions in /s fro te velocity selector is (a) 0 7 / s (b) 0 4 / s (c) 0 5 / s (d) 0 / s xaple: V By using v ; were 0 V / B d 0 v 0 / s. An electron and a poton ave sae wavelengt. It p is te oentu of electron and te energy of poton. Te agnitude of p/ in S.I. unit is

9 Solution : (b) xaple: 7 Solution : (b) genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays 9 (a) (b) (c) (d) c (for electron) or p and (for poton) p p s / c / s Te energy of a poton is equal to te kinetic energy of a proton. Te energy of te poton is. Let be te de-broglie wavelengt of te proton and be te wavelengt of te poton. Te ratio / is proportional to [UPSAT 003; IIT-J (Screening) 004] 0 / (a) (b) (c) (d) c For poton. (i) and For proton.(ii) Terefore / c /. xaple: 8 Te de-broglie wavelengt of an electron aving 80eV of energy is nearly ( ev. 0 J, Mass of 3 34 electron 9 0 kg and Plank's constant. 0 J-sec) (a) 40 Å (b) 0.4 Å (c) 4 Å (d).4 Å Solution : (d) By using. 7. If energy is 80 ev ten accelerating potential difference will be 80 V. So V Å. 80 xaple: 9 3 Te kinetic energy of electron and proton is 0 J. Ten te relation between teir de-broglie wavelengts is (a) p e (b) p e (c) p e (d) p e Solution : (a) xaple: 0 Solution : (b) xaple: By using = 0 3 J = Constant for bot particles. Hence Since so. p e p e Te energy of a proton and an particle is te sae. Ten te ratio of te de-broglie wavelengts of te proton and te is [RPT 99] (a) : (b) : (c) : 4 (d) 4 : proton By using ( sae). particle p 0 Te de-broglie wavelengt of a particle accelerated wit 50 volt potential is 0. If it is accelerated by 00 volts p.d., its wavelengt will be [RPT 988] (a) 0.5 Å (b) 0.5 Å (c).5 Å (d) Å 0 Solution : (b) By using V 0 00 V V 50 = 0.5 Å. xaple: Te de-broglie wavelengt of an electron in an orbit of circuference r is [MP PT 987] (a) r (b) r (c) / r (d) / 4r Solution : (a) According to Bor's teory v r n r n n v For n = = r xaple: 3 Te nuber of potons of wavelengt 540 n eitted per second by an electric bulb of power 00W is 34 (taking 0 J-sec) [Kerala (ngg.) 00] (a) 00 (b) 000 (c) (d) 3 0 xaple: 4 Solution : (a) 9 P By using n 3 0 c A steel ball of ass kg is oving wit a velocity /s. Ten its de-broglie waves lengt is equal to (a) (b) / (c) Zero (d) / By using. v 9

10 0 lectron, Poton, Potoelectric ffect and X-rays xaple: 5 Solution : (b) xaple: xaple: 7 Solution : (b) xaple: 8 Solution : (a) xaple: 9 Solution : (a) xaple: 0 Te de-broglie wavelengt associated wit a ydrogen ato oving wit a teral velocity of 3 k/s will be (a) Å (b) 0. Å (c). Å (d) Å By using 0. Å v 7 3 rs Wen te oentu of a proton is canged by an aount P 0, te corresponding cange in te de-broglie wavelengt is found to be 0.5%. Ten, te original oentu of te proton was [CPMT 00] (a) p 0 (b) 00 p 0 (c) 400 p 0 (d) 4 p 0 p p p p = 400 p 0. p p p p If te electron as sae oentu as tat of a poton of wavelengt 500Å, ten te velocity of electron in /sec is given by (a) 0 3 (b) (c) (d) v v = /s. v Te de-broglie wavelengt of a neutron at 7 o C is. Wat will be its wavelengt at 97 o C (a) / (b) / 3 (c) / 4 (d) / 9 neutron T T T (73 97) 00 (73 7) 300. Te de-broglie wavelengt of a veicle is. Its load is canged suc tat its velocity and energy bot are doubled. Its new wavelengt will be (a) (b) (c) (d) 4 v and v v wen v and bot are doubled, reains uncanged i.e. ' =. In Toson ass spectrograp wen only electric field of strengt 0 kv/ is applied, ten te displaceent of te bea on te screen is c. If lengt of plates = 5 c, distance fro centre of plate to te screen = 0 c and velocity of ions = 0 /s, ten q/ of te ions is (a) 0 C/kg (b) 0 7 C/Kg (c) 0 8 C/kg (d) 0 C/kg qld By using y ; were y = deflection on screen due to electric field only v q yv 0 (0 ) 8 0 C / kg. LD xaple: Te iniu intensity of ligt to be detected by uan eye is 0 W /. Te nuber of potons of wavelengt entering te eye, wit pupil area 0, per second for vision will be nearly (a) 00 (b) 00 (c) 300 (d) 400 P By using I ; were P = radiation power A n c n IA P I A IA t t c n 0 0 Hence nuber of potons entering per sec te eye t = 300. xaple. A particle of ass M at rest decays into two particles of asses and, aving non-zero velocities. Te ratio of te de-broglie wavelengts of te particles, / is [IIT-J 999] (a) / (b) / (c).0 (d) / According to conservation of oentu i.e. p p Hence fro p p p M p p

11 lectron, Poton, Potoelectric ffect and X-rays Solution : (a) Te curve drawn between velocity and frequency of poton in vacuu will be a [MP PT 000] (a) Straigt line parallel to frequency axis (b) Straigt line parallel to velocity axis (c) Straigt line passing troug origin and aking an angle of 45 o wit frequency axis (d) Hyperbola Velocity of poton (i.e. ligt) doesn t depend upon frequency. Hence te grap between velocity of poton and frequency will be as follows. Velocity of poton (c) Frequency Poto-electric ffect. It is te penoenon of eission of electrons fro te surface of etals, wen ligt radiations (lectroagnetic radiations) of suitable frequency fall on te. Te eitted electrons are called potoelectrons and te current so produced is called potoelectric current. Tis effect is based on te principle of conservation of energy. () Ters related to potoelectric effect (i) Work function (or tresold energy) (W 0) : Te iniu energy of incident radiation, required to eject te electrons fro etallic surface is defined as work function of tat surface. c W0 0 Joules ; 0 = Tresold frequency; 0 = Tresold wavelengt Work function in electron volt W 0(eV) Note : 0 c 375 e 0 ( Å) 0 By coating te etal surface wit a layer of bariu oxide or strontiu oxide it's work function is lowered. (ii) Tresold frequency ( 0) : Te iniu frequency of incident radiations required to eject te electron fro etal surface is defined as tresold frequency. If incident frequency < 0 No potoelectron eission (iii) Tresold wavelengt ( 0) : Te axiu wavelengt of incident radiations required to eject te electrons fro a etallic surface is defined as tresold wavelengt. If incident wavelengt > 0 No potoelectron eission () instein's potoelectric equation According to instein, potoelectric effect is te result of one to one inelastic collision between poton and electron in wic poton is copletely absorbed. So if an electron in a etal absorbs a poton of energy (= ), it uses te energy in tree following ways. (i) Soe energy (say W) is used in sifting te electron fro interior to te surface of te etal. (ii) Soe energy (say W 0) is used in aking te surface electron free fro te etal. (iii) Rest energy will appear as kinetic energy (K) of te eitted potoelectrons. Hence = W + W 0 + K For te electrons eitting fro surface W = 0 so kinetic energy of eitted electron will be ax. Hence = W 0 + K ax ; Tis is te instein's potoelectric equation (3) xperiental arrangeent to observe potoelectric effect Wen ligt radiations of suitable frequency (or suitable wavelengt and suitable energy) falls on plate P, potoelectrons are eitted fro P. P K e e W Radiation e e e e e e e e e Q e e e Metal Incident poton Work function V A Batter

12 3 genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays (i) If plate Q is at zero potential w.r.t. P, very sall current flows in te circuit because of soe electrons of ig kinetic energy are reacing to plate Q, but tis current as no practical utility. (ii) If plate Q is kept at positive potential w.r.t. P current starts flowing troug te circuit because ore electrons are able to reac upto plate Q. (iii) As te positive potential of plate Q increases, current troug te circuit increases but after soe tie constant current flows troug te circuit even positive potential of plate Q is still increasing, because at tis condition all te electrons eitted fro plate P are already reaced up to plate Q. Tis constant current is called saturation current. (iv) To increase te potoelectric current furter we will ave to increase te intensity of incident ligt. Potoelectric current (i) depends upon (a) Potential difference between electrodes (till saturation) I (b) Intensity of incident ligt (I) (c) Nature of surface of etal (v) To decrease te potoelectric current plate Q is aintained at negative potential w.r.t. P, as te anode Q is ade ore and ore negative, fewer and fewer electrons will reac te catode and te potoelectric current decreases. (vi) At a particular negative potential of plate Q no electron will reac te plate Q and te current will becoe zero, tis negative potential is called stopping potential denoted by V 0. (vii) If we increase furter te energy of incident ligt, kinetic energy of potoelectrons increases and ore negative potential sould be applied to stop te electrons to reac upto plate Q. Hence ev. Note : 0 K ax Stopping potential depends only upon frequency or wavelengt or energy of incident radiation. It doesn't depend upon intensity of ligt. We ust reeber tat intensity of incident ligt radiation is inversely proportional to te square of distance between source of ligt and potosensitive plate P i.e., I so I i ) d d Iportant forulae 0 Kax K ax ev0 ( 0) v ax ( 0 ) v 0 K ax v ax ev0 c c v 0 0 ax ax ( 0 ) c 0 c V 0 ( 0 ) 375 e e 0 0 (4) Different graps (i) Grap between potential difference between te plates P and Q and potoelectric current i I3 I i 0 i I 3 > > V0 (ii) Grap between axiu V kinetic energy / stopping potential of potoelectrons and frequency of incident ligt For different intensities of incident ligt V0 V0 V0 3 V For different Frequencies of incident ligt Kax V0 Potoelectric Cell. W0 Slope = tan = Slope = tan = /e

13 Output genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays 3 A device wic converts ligt energy into electrical energy is called potoelectric cell. It is also known as potocell or electric eye. Potoelectric cell are ainly of tree types Poto-eissive cell Poto-conductive cell Poto-voltaic cell It consists of an evacuated glass or quartz bulb containing anode A and catode C. Te catode is sei-cylindrical etal on wic a layer of poto-sensitive aterial is coated. It is based on te principle tat conductivity of a seiconductor increases wit increase in te intensity of incident ligt. Galvanoeter or Wen ligt incident Micro on te catode, it eits poto-electrons aeter wic are attracted by te A anode. Te potoelectrons + constitute a sall current wic flows troug te external circuit. Note : In tis, Seleniu a tin layer R of Output soe seiconductor Metal layer (as seleniu) is placed below a transparent foil of soe etal. Tis cobination is fixed over an iron plate. Wen ligt is incident on te transparent foil, te electrical resistance of te seiconductor layer is reduced. Hence a current starts flowing in te battery circuit connected. It consists of a Cu plate coated wit a tin layer of cuprous oxide (Cu O). On tis plate is laid a sei transparent tin fil of silver. C Wen Seiconducting ligt fall, layer of CuO te electrons R eitted Metal fro layer te of layer Cu of Cu O and ove towards te silver fil. Ten te silver fil becoes negatively carged and copper plate becoes positively carged. A potential difference is set up between tese two and current is set up in te external resistance. Te potoelectric current can be increased by filling soe inert gas like Argon into te bulb. Te potoelectrons eitted by catode ionise te gas by collision and ence te current is increased. Copton effect Te scattering of a poton by an electron is called Copton effect. Te energy and oentu is conserved. Scattered poton will ave less energy (ore wavelengt) as copare to incident poton (less wavelengt). Te energy lost by te poton is taken by electron as kinetic energy. Te cange in wavelengt due to Copton effect is called Copton sift. Copton sift f i ( cos ) c 0 Ligt A C Surface fil Copton scattering Target electron at rest Incident Note : Copton effect sows tat poton ave oentu. i X-rays. X-rays was discovered by scientist Rontgen tat's wy tey are also called Rontgen rays. Rontgen discovered tat wen pressure inside a discarge tube kept 0 3 of Hg and potential difference is 5 kv ten soe unknown radiations (X-rays) are eitted by anode. () Production of X-rays Tere are tree essential requireents for te production of X-rays (i) A source of electron (ii) An arrangeent to accelerate te electrons (iii) A target of suitable aterial of ig atoic weigt and ig elting point on wic tese ig speed electrons strike. () Coolidge X-ray tube It consists of a igly evacuated glass tube containing catode and target. Te catode consist of a tungsten filaent. Te filaent is coated wit oxides of bariu or strontiu to ave an eission of electrons even at low teperature. Te filaent is surrounded by a olybdenu cylinder kept at negative potential w.r.t. te target. Scattered poton f Recoil electron A Transparent fil of silver

14 4 lectron, Poton, Potoelectric ffect and X-rays Te target (it's aterial of ig atoic weigt, ig elting point and ig teral conductivity) ade of tungsten or olybdenu is ebedded in a copper block. Te face of te target is set at 45 o to te incident electron strea. Te filaent is eated by passing te current F troug it. A ig potential difference ( 0 kv to 80 kv) is Filaent W applied between te target and catode to accelerate te electrons Target wic are eitted by filaent. Te strea of Window X-rays igly energetic electrons are focussed on te target. Most of te energy of te electrons is converted into eat (above 98%) and only a fraction of te energy of te electrons (about %) is used to produce X-rays. During te operation of te tube, a uge quantity of eat is produced in tis target, tis eat is conducted troug te copper anode to te cooling fins fro were it is dissipated by radiation and convection. (i) Control of intensity of X-rays : Intensity iplies te nuber of X-ray potons produced fro te target. Te intensity of X-rays eitted is directly proportional to te electrons eitted per second fro te filaent and tis can be increased by increasing te filaent current. So intensity of X-rays Filaent current (ii) Control of quality or penetration power of X-rays : Quality of X-rays iplies te penetrating power of X-rays, wic can be controlled by varying te potential difference between te catode and te target. For large potential difference, energy of bobarding electrons will be large and ence larger is te penetration power of X-rays. Depending upon te penetration power, X-rays are of two types Hard X-rays Soft X-rays More penetration power Less penetration power More frequency of te order of 0 9 Less frequency of te order of 0 Hz Hz Lesser wavelengt range (0.Å 4Å) More wavelengt range (4Å 00Å) Note : Production of X-ray is te reverse penoenon of potoelectric effect. (3) Properties of X-rays (i) X-rays are electroagnetic waves wit wavelengt range 0.Å 00Å. (ii) Te wavelengt of X-rays is very sall in coparison to te wavelengt of ligt. Hence tey carry uc ore energy (Tis is te only difference between X-rays and ligt) (iii) X-rays are invisible. (iv) Tey travel in a straigt line wit speed of ligt. (v) X-rays are easured in Rontgen (easure of ionization power). (vi) X-rays carry no carge so tey are not deflected in agnetic field and electric field. (vii) Gaa rays X - rays UV rays Lead caber C V T (viii) Tey used in te study of crystal structure. (ix) Tey ionise te gases (x) X-rays do not pass troug eavy etals and bones. (xi) Tey affect potograpic plates. (xii) Long exposure to X-rays is injurious for uan body. (xiii) Lead is te best absorber of X-rays. (xiv) For X-ray potograpy of uan body parts, BaSO 4 is te best absorber. (xv) Tey produce potoelectric effect and Copton effect (xvi) X-rays are not eitted by ydrogen ato. (xvii) Tese cannot be used in Radar because tey are not reflected by te target. (xviii) Tey sow all te iportant properties of ligt rays like; reflection, refraction, interference, diffraction and polarization etc. (4) Absorption of X-rays X-rays are absorbed wen tey incident on substance. Anode Water I0 ergent X-rays Incident X- I

15 Intensit y Intensity of eergent X-rays I I 0 e x So intensity of absorbed X-rays ' 0 ( x I I I I e ) 0 genius PHYSICS lectron, Poton, Potoelectric ffect and X-rays 5 were x = tickness of absorbing ediu, = absorption coefficient I Note : Te tickness of ediu at wic intensity of eergent X-rays becoes alf i.e. I' is called alf value tickness (x /) and it is given as x /. Classification of X-rays. In X-ray tube, wen ig speed electrons strikes te target, tey penetrate te target. Tey loses teir kinetic energy and coes to rest inside te etal. Te electron before finally being stopped akes several collisions wit te atos in te target. At eac collision one of te following two types of X-rays ay get for. () Continuous X-rays As an electron passes close to te positive nucleus of ato, te electron is deflected fro it's pat as sown in figure. Tis results in deceleration of te electron. Te loss in energy of te electron during deceleration is eitted in te for of X-rays. Te X-ray potons eitted so for te continuous X-ray spectru. Note : Continuos X-rays are produced due to te penoenon called "Bresstralung". It eans slowing down or braking radiation. Miniu wavelengt Wen te electron looses wole of it's energy in a single collision wit te ato, an X-ray poton of c axiu energy ax is eitted i.e. v ev ax in were v = velocity of electron before collision wit target ato, V = potential difference troug wic electron is accelerated, c = speed of ligt = /s ev Maxiu frequency of radiations (X-rays) ax Miniu wave lengt = cut off wavelengt of X-ray c 375 in Å ev V Wavelengt of continuous X-ray poton ranges fro certain iniu ( in) to infinity. Note : e + X-ray poton ax logeax in logeax Intensity wavelengt grap V logev V logev Te continuous X-ray spectra consist of all te wavelengts over a given range. Tese wavelengt are of different intensities. Following figure sows te intensity variation of different wavelengts for various accelerating voltages applied to X-ray tube. For eac voltage, te intensity curve starts at a particular iniu wavelengt ( in). Rises rapidly to a axiu and ten drops gradually. Te wavelengt at wic te intensity is axiu depends on te accelerating voltage, being sorter for iger voltage and vice-versa. () Caracteristic X-rays Few of te fast oving electrons aving ig velocity penetrate te surface atos of te target aterial and knock out te tigtly bound electrons even fro te inner ost sells of te ato. Now wen te electron is knocked out, a vacancy is created at tat place. To fill tis vacancy electrons fro iger sells jup to fill te created vacancies, we know tat wen an electron jups fro a iger energy orbit to lower energy orbit, it radiates energy ( ). Tus tis energy difference is radiated in te for of X-rays of very sall but definite wavelengt wic depends upon te target aterial. Te X-ray spectru consist of sarp lines and is called caracteristic X-ray spectru. e Y in Wave lengt 30 kv 0 kv 0 kv e e X-ray poton

16 lectron, Poton, Potoelectric ffect and X-rays K, L, M, series If te electron striking te target eject an electron fro te K-sell of te ato, a vacancy is crated in te K-sell. Iediately an electron fro one of te outer sell, say L-sell jups to te K-sell, eitting an X-ray poton of energy equal to te energy difference between te two sells. Siilarly, if an electron fro te M-sell jups to te K-sell, X- ray poton of iger energy is eitted. Te X-ray potons eitted due to te jup of electron fro te L, M, N sells to te K-sells gives K, K, K lines of te K-series of te spectru. If te electron striking te target ejects an electron fro te L- sell of te target ato, an electron fro te M, N.. sells jups to te L-sell so tat X-rays potons of lesser energy are eitted. Tese potons for te lesser energy eission. Tese potons for te L-series of te spectru. In a siilar way te foration of M series, N series etc. ay be explained. nergy and wavelengt of different lines Series Transition nergy Wavelengt K L K L K K c K L Note : () (3) () M K M K K (3) () M L M L L () K L K M M L c c K K L 375 Å ( ) ev L K 375 ( ) ev M K Å 375 Å ( ) ev Te wavelengt of caracteristic X-ray doesn't depend on accelerating voltage. It depends on te atoic nuber (Z) of te target aterial. K L M and K L M K L K O N M L n=5 n=4 M M M n=3 M-series L L L L n= L-series K K K K n= K-series Intensity-wavelengt grap At certain sarply defined wavelengts, te intensity of X-rays is very large as arked K, K. As sown in figure. Tese X-rays are known as caracteristic X-rays. At oter wavelengts te intensity varies gradually and tese X-rays are called continuous X-rays. Mosley's law Mosley studied te caracteristic X-ray spectru of a nuber of a eavy eleents and concluded tat te spectra of different eleents are very siilar and wit increasing atoic nuber, te spectral lines erely sift towards iger frequencies. Intensit in K K L L L K- L-series Wavelengt k k Z He also gave te following relation a( Z b) were = Frequency of eitted line, Z = Atoic nuber of target, a = Proportionality constant, b = Screening constant. Note : a and b doesn't depend on te nature of target. Different values of b are as follows

17 lectron, Poton, Potoelectric ffect and X-rays 7 b = for K-series b = 7.4 for L-series b = 9. for M-series (Z b) is called effective atoic nuber. More about Mosley's law (i) It supported Bor's teory (ii) It experientally deterined te atoic nuber (Z) of eleents. (iii) Tis law establised te iportance of ordering of eleents in periodic table by atoic nuber and not by atoic weigt. (iv) Gaps in Moseley's data for A = 43,, 7, 75 suggested existence of new eleents wic were later discovered. (v) Te atoic nubers of Cu, Ag and Pt were establised to be 9, 47 and 78 respectively. (vi) Wen a vacancy occurs in te K-sell, tere is still one electron reaining in te K-sell. An electron in te L-sell will feel an effective carge of (Z )e due to + Ze fro te nucleus and e fro te reaining K-sell electron, because L-sell orbit is well outside te K-sell orbit. (vii) Wave lengt of caracteristic spectru c Rc( Z b) n n R( Z b) n n (viii) If transition takes place fro n = to n = (K - line) (a) a (b) K 3RC Hz 3RC 5 RC ( Z ) ( Z ).47 0 ( Z ) 4 (c) In general te wavelengt of all te K-lines are given by Wile for K line (d) K Å ( Z ) K 0.( Z ) ev K Hz and energy of X-ray radiations. R( Z ) were n =, 3, 4,. n Uses of X-rays (i) In study of crystal structure : Structure of DNA was also deterined using X-ray diffraction. (ii) In edical science. (iii) In radiograp (iv) In radio terapy (v) In engineering (vi) In laboratories (vii) In detective departent (viii) In art te cange occurring in old oil paintings can be exained by X-rays.

18 8 lectron, Poton, Potoelectric ffect and X-rays Concepts Nearly all etals eits potoelectrons wen exposed to UV ligt. But alkali etals like litiu, sodiu, potassiu, rubidiu and cesiu eit potoelectrons even wen exposed to visible ligt. Oxide coated filaent in vacuu tubes is used to eit electrons at relatively lower teperature. Conduction of electricity in gases at low pressure takes because colliding electrons acquire iger kinetic energy due to increase in ean free pat. Kinetic energy of catode rays depends on bot voltage and work function of catode. Potoelectric effect is due to te particle nature of ligt. Hydrogen ato does not eit X-rays because it's energy levels are too close to eac oter. Te essential difference between X-rays and of -rays is tat, -rays eits fro nucleus wile X-rays fro outer part of ato. Tere is no tie delay between eission of electron and incidence of poton i.e. te electrons are eitted out as soon as te ligt falls on etal surface. If ligt were wave (not potons) it will take about an year take about an year to eject a potoelectron out of te etal surface. Doze of X-ray are easured in ters of produced ions or free energy via ionisaiton. Safe doze for uan body per week is one Rontgen (One Rontgon is te aount of X-rays wic eits J free energy troug ionization of g air at NTP xaple xaple: Te work function of a substance is 4.0 ev. Te longest wavelengt of ligt tat can cause potoelectron eission fro tis substance is approxiately [AI 004] (a) 540 n (b) 400 n (c) 30 n (d) 0 n By using 0 0 = Å ~ 30 n W0 ( ev ) 4 xaple: 3 Poto-energy ev are incident on a surface of work function. ev. Wat are te stopping potential [MP PMT 004] (a) 5V (b).9 V (c) 3.9 V (d) 8. V By using instein's equation = W 0 + K ax. Kax Kax 3. 9 ev K ax Also V0 3.9 V. xaple: 4 Wen radiation of wavelengt is incident on a etallic surface te stopping potential is 4.8 volts. If te sae surface is illuinated wit radiation of double te wavelengt, ten te stopping potential becoes. volts. Ten te tresold wavelengt for te surface is (a) (b) 4 (c) (d) 8 c Solution : (b) By using V 0 e 0 xaple: 5 c c 4.8 (i) and. (ii) e 0 e 0 Fro equation (i) and (ii) 0 4. Wen radiation is incident on a potoelectron eitter, te stopping potential is found to be 9 volts. If e/ for te electron is.8 0 Ckg te axiu velocity of te ejected electrons is (a) 5 0 s (b) s (c).8 0 s (d) s e v ax ev0 v ax. V / s. xaple: Te lowest frequency of ligt tat will cause te eission of potoelectrons fro te surface of a etal (for wic work function is.5 ev) will be [JIPMR 00] (a) Hz (b) 4 0 Hz (c) Hz 0 (d) 4 0 Hz Tresold wavelengt 0 W0 ( ev) c so iniu frequency Hz

19 lectron, Poton, Potoelectric ffect and X-rays 9 xaple: 7 Ligt of two different frequencies wose potons ave energies ev and.5 ev respectively, successively illuinates a etal of work function 0.5 ev. Te ratio of axiu kinetic energy of te eitted electron will be (a) : 5 (b) : 4 (c) : (d) : Solution : (b) ( Kax) By using Kax W0. ( Kax) xaple: 8 Potoelectric eission is observed fro a etallic surface for frequencies and of te incident ligt rays ( ). If te axiu values of kinetic energy of te potoelectrons eitted in te two cases are in te ratio of : k, ten te tresold frequency of te etallic surface is [AMCT (ngg.) 00] (a) k k (b) (c) (d) k k k k Solution : (b) By using 0 k ax ( 0 ) k and ( 0 ) k 0 k k Hence 0 0 k k k xaple: 9 5 Ligt of frequency 8 0 Hz is incident on a substance of potoelectric work function.5 ev. Te axiu kinetic energy of te eitted potoelectrons is [AFMC 00] (a) 7 ev (b) ev (c) 7 ev (d) 37 ev 34 5 nergy of incident poton J 33 ev. xaple: 30 Solution : (d) xaple: 3 Solution : (a) Fro W 0 Kax K ax W ev 7 ev. A poto cell is receiving ligt fro a source placed at a distance of. If te sae source is to be placed at a distance of, ten te ejected electron [MNR 98; UPSAT 000, 00] (a) Moves wit one-fourt energy as tat of te initial energy (b) Moves wit one fourt of oentu as tat of te initial oentu (c) Will be alf in nuber (d) Will be one-fourt in nuber Nuber of potons Intensity (distance) N d N N N N d N 4. Wen yellow ligt incident on a surface no electrons are eitted wile green ligt can eit. If red ligt is incident on te surface ten [MNR 998; MH CT 000; MP PT 000] (a) No electrons are eitted (b) Potons are eitted (c) lectrons of iger energy are eitted (d) lectrons of lower energy are eitted Green Yellow Red According to te question Green is te axiu wavelengt for wic potoelectric eission takes place. Hence no eission takes place wit red ligt. xaple: 3 Wen a etal surface is illuinated by ligt of wavelengts 400 n and 50 n te axiu velocities of te potoelectrons ejected are v and v respectively. Te work function of te etal is ( = Planck's constant, c = velocity of ligt in air) [MCT (ngg.) 000] (a) c 0 J (b).5c 0 J (c) c 0 J (d) 0.5c 0 J c Solution : (a) By using W 0 Kax W 0 v c c W 9 0 v (i) and W 0 (v) (ii) Fro equation (i) and (ii) W c 0. 0 J xaple: 33 Te work functions of etals A and B are in te ratio :. If ligt of frequencies f and f are incident on te surfaces of A and B respectively, te ratio of te axiu kinetic energies of potoelectrons eitted is (f is greater tan tresold frequency of A, f is greater tan tresold frequency of B) [AMCT (Med.) 000] (a) : (b) : (c) : 3 (d) : 4 Solution : (b) By using W 0 Kax A f WA K A and B ( f) WB KB WA K A WA So, (i) also it is given tat..(ii) WB K B WB K A Fro equation (i) and (ii) we get. K B xaple: 34 Wen a point source of onocroatic ligt is at a distance of 0. fro a potoelectric cell, te cut-off voltage and te saturation current are 0. volt and 8 A respectively. If te sae source is placed 0. away fro te potoelectric cell, ten [IIT-J 99; MP PMT 999]

20 0 lectron, Poton, Potoelectric ffect and X- rays (a) Te stopping potential will be 0. V (c) Te saturation current will be A Solution : (b) Potoelectric current (i) Intensity (distance) (b) Te stopping potential will be 0. V (d) Te saturation current will be 8 A. If distance becoes 0. (i.e. tree ties) so current becoes xaple: 35 Solution : (d) ties i.e. A. 9 Also stopping potential is independent of intensity i.e. it reains 0. V. In a potoeissive cell wit exciting wavelengt, te fastest electron as speed v. If te exciting wavelengt is canged to 3 / 4, te speed of te fastest eitted electron will be [CBS 998] (a) Fro / v (3 / 4) (b) v W 0 ax 0 v ax / / v (4 / 3) (c) Less ten v (4 / 3) (d) Greater ten W (were c ) / v (4 / 3) xaple: 3 Solution : (a) 3 If wavelengt of incident ligt carges fro to (decreases) 4 Let energy of incident ligt carges fro to ' and speed of fastest electron canges fro v to v ten W0 v..(i) and As 4 ' ence 3 / ' W0 v'.(ii) 4 3 W0 v' 4 v ' 3 / W W0 4 v ' X v so v' v. 3 / Te iniu wavelengt of X-rays produced in a coolidge tube operated at potential difference of 40 kv is (a) 0.3Å (b) 3.Å (c) 3Å (d) 3Å 375 in Å 0.3 Å / 0 / [BCC 003] xaple: 37 Te X-ray wavelengt of L line of platinu (Z = 78) is.30 Å. Te X ray wavelengt of L a line of Molybdenu (Z = 4) is [AMCT (ngg.) 000] (a) 5.4Å (b) 4.0Å (c).70å (d).35 Å Solution : (a) Te wave lengt of L line is given by R( z 7.4) 3 ( z 7.4) ( z ( z Tricky exaple: 3 xaple: 38 Solution : (d) 7.4) 7.4).30 (4 7.4) (78 7.4) 5.4Å. Te cut off wavelengt of continuous X-ray fro two coolidge tubes operating at 30 kv but using different target aterials (olybdenu Z= 4 and tungsten Z = 74) are (a) Å, 3Å (b) 0.3 Å, 0. Å (c) 0.44 Å, 0.8 Å (d) 0.44 Å, 0.44 Å Cut off wavelengt of continuous X-rays depends solely on te voltage applied and does not depend on te aterial of te target. Hence te two tubes will ave te sae cut off wavelengt. 34 c c Ve or Å. 3 9 Ve

21 lectron, Poton, Potoelectric ffect and X-rays Tricky exaple: 4 Solution : (b) Two potons, eac of energy.5ev are siultaneously incident on te etal surface. If te work function of te etal is 4.5 ev, ten fro te surface of etal (a) Two electrons will be eitted will be eitted (c) One electron will be eitted will be eitted (b) Not even a single electron (d) More tan two electrons Potoelectric effect is te penoenon of one to one elastic collision between incident poton and an electron. Here in tis question one electron absorbs one poton and gets energy.5 ev wic is lesser tan 4.5 ev. Hence no potoelectron eission takes place. Tricky exaple: 5 In X-ray tube wen te accelerating voltage V is alved, te difference between te wavelengt of K line and iniu wavelengt of continuous X-ray spectru (a) Reains constant ties (b) Becoes ore tan two (c) Becoes alf (d) Becoes less tan two ties K in wen V is alved in becoes two ties but K a reains te sae. ' in ( ) K ' ( ) Tricky exaple: K a Molybdenu eits K -potons of energy 8.5 kev and iron eits K potons of energy 34.7 kev. Te ties taken by a olybdenu K poton and an iron K poton to travel 300 are (a) (3 s, 5 s) (b) (5 s, 3s) (c) ( s, s) (d) ( s, 5s) Poton ave te sae speed watever be teir energy, frequency, wavelengt, and origin. tie of travel of eiter poton s s 8 3 0