DUAL NATURE OF RADIATION AND MATTER

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1 DUAL NATURE OF RADIATION AND MATTER Important Points: 1. J.J. Tomson and Sir William Crookes studied te discarge of electricity troug gases. At about.1 mm of Hg and at ig voltage invisible streams called catode rays are emitted. J.J. Tomson called tem streams of negative corpuscles. Jonston Stony suggested te name Electron. Tus te electron was discovered.. Poto Electric Effect:. Wen ligt of suitable frequency is incident on metal surface, electrons are emitted from tat surface. Tis penomenon is called poto-electric effect. Te minimum energy required to remove a poto electron from a metal surface is called work function of te metal (W). W υ c 14 W ev λ λ ( A ) 3. Einstein s Poto Electric Equation E W + KE 1 υ W + mv v Maximum velocity of emitted potoelectron a. Te minimum negative potential given to te collector. At wic potoelectric current becomes zero is called stopping potential ( V ). Te above equation can also be written as υ υ + ev

2 4. Laws of Poto-Electric Effect: a. Tis is instantaneous penomenon b. K. E max is independent of intensity of incident radiation but directly proportional to frequency of incident radiation. c. Te poto electric current is independent of frequency of incident radiation but directly proportional to intensity of incident radiation. d. Te frequency of incident radiation of below te tresold frequency of metal no poto electrons are emitted. 5. De Broglie Hypoteses: Te waves associated wit moving particles are called matter waves (or) de-broglie waves. De Broglie predicted tat te wavelengt of tese waves is given by λ p mv 1.9 A mev v 6. Poton as bot wave and particle nature. Its rest mass is zero. 7. Te wave nature of electron can be explained by Davisson and Germer Experiment.

3 Very Sort Answer Questions 1. Wat are Catode Rays? A. Catode rays are a stream of negatively carged particles produced in a discarge tube at low pressure about.1 mm of Hg and ig potential difference above KV.. Wat is te important fact did Millikan s experiment establis? A. Importance of Millikan s Experiment: Carge is always quantized. Te carge on any particle is only an integral multiple of te carge of te electron. 3. Wat is Work Function? A. Te minimum amount of energy required just to eject an electron from te surface of a metal is called te work function of te metal. It is generally denoted by φ and measured in ev. c Work function. W v Were v is tresold frequency and λ is Tresold λ wavelengt. 4. Wat is Poto Electric Effect? A. Poto electric effect is te penomenon of emission of electrons by metals wen illuminated by ligt of suitable frequency. 5. Give examples of Potosensitive Substances. Wy are tey called so? A. Litium, Sodium, Potassium, Cesium and Rubidium are some examples of poto sensitive metals, because te work function of tese metals is very low and tey are very sensitive even to visible ligt also to emit electrons.

4 6. Write down Einstein s Poto Electric Equation? A. Poton energy is utilized in two ways. Some part of energy is utilized to remove te electron from te metal surface (Work Function W ) and remaining part of energy appears as kinetic energy of an electron. Poton energy work function + kinetic energy. 1 υ W m + υ max 7. Write down te de-broglie s relation and explain te terms terein? A. According to Louis de Broglie s ypotesis, every moving particle will ave some wave associated wit it. Tey are called matter waves or de Broglie Waves. Te ratio between te Planck s constant and te momentum of te particle is called De Broglie Wavelengt. λ p mv Were v velocity of te particle and Planck s constant. 8. State Heisenberg's Uncertainty Principle? A. Heisenberg's Uncertainty Principle: According to Heisenberg s Uncertainty Principle, it is impossible to measure simultaneously bot te position and te momentum of te particle. Let x and p be te uncertainty in te simultaneous measurement of te position and momentum of te particle, ten x p ; were Planck s constant ( π 1.5 J sec ). and J-s is te π

5 Sort Answer Questions 1. Wat is te effect of (i) Intensity of Ligt (ii) Potential on Potoelectric Current? A. (i) Effect of Intensity of Ligt: Te number of potoelectrons emitted per second (potoelectric current) is proportional to te intensity of te incident radiation. (ii) Effect of Potential: For a given frequency of incident radiation, te stopping potential is independent of intensity of te incident radiation. Hence te number of potoelectrons emitted per second (potoelectric current) is independent potential.. Describe an experiment to study te effect of frequency of incident radiation on A. Stopping Potential? Wen a monocromatic ligt of suitable frequency from te source S after being filtered by a filter attaced to a window W, fall on potosensitive plate C (emitter), poto electrons are emitted tese electrons are accelerated towards te collector plate A.Te emission of electrons causes flow of current called poto electric current in te circuit. Micro ammeter measures poto electric current. Te plate A can be maintained at desired positive or negative potential wit respect to emitter by using a battery. By taking radiations of different frequencies but of same intensity, te variation of poto electric current wit potential is sown in below grap.

6 Saturation current From Grap: 1) Te value of stopping potential is different for radiations of different frequencies. ) Greater te frequency of incident ligt, greater is te stopping potential. V3 > V > V1 3) Value of saturation current depends on intensity but not on frequency of radiation. υ and V Grap: 1) For a given poto sensitive material, stopping potential varies linearly wit frequency of radiation. ) For a given poto sensitive material, tere is certain minimum cut off frequency for wic stopping potential equal to zero. ' Since υ > υ, te tresold frequency is more for metal B tan for metal A. 3. Summarize te poton picture of electromagnetic radiation? A. Poton picture of Electromagnetic Radiation: (i) In interaction of radiation wit matter, radiation beaves as if it is made up of particles called potons. (ii) Every poton as energy E ν and momentum ν p and C is te speed of ligt. c (iii) All potons of ligt of particular frequency and wavelengt ave same energy and momentum irrespective of te intensity. (iv) Potons are electrically neutral and tey are not deflected by electric and magnetic fields.

7 (v) In a poton - particle collision, te total energy and total momentum are conserved. But te number of potons may not be conserved. 4. Wat is te de Broglie wavelengt of a ball of mass.1 kg moving wit a speed of m/s? Wat can we infer from tis result? A. m.1 kg; v m/s 6.63 λ.765 mv.1 Te de Broglie wavelengt of a ball is about m 19 times te size of proton.

8 Long Answer Questions 1. How did Einstein s Potoelectric Equation explain te effect of intensity and potential on potoelectric current? How did tis equation account for te effect of frequency of incident radiation on stopping potential? A. Einstein s Potoelectric Equation: According to Einstein, wen a poton strikes an electron, ten its entire energy ( E ν ) is utilized in two ways. (i) A part of incident energy is used to just to eject an electron from te surface called te work function ( φ ) of te metal. (ii) Remaining part of energy is converted as te kinetic energy of te ejected electron. 1 υ φ + mv Effect of te Intensity: For a given frequency of intensity of ligt, tere is saturation potocurrent. Tis saturation potocurrent is proportional to te intensity of te ligt. Potocurrent Intensity Intensity of ligt is proportional to te number of potons per unit area per unit time. Greater te number of potons, greater te potoelectrons (for ν > ν ). Hence potocurrent is proportional to te intensity of ligt. Effect of Potential: For a given poto metal ( φ constant), te kinetic energy of te ejected electron depends on te frequency of incident ligt. Greater te frequency, greater te kinetic energy. Te value of te retarding potential difference to be applied between te surface of a potosensitive plate and te electrode of te collector, wic is just sufficient to stop te most energetic poto electrons is called stopping potential. Te stopping potential or cut off potential (V s ) is measure of te maximum K.E. of te emitted potoelectrons.

ev s 1 K mv Te value of stopping potential difference is independent of te ligt intensity. Stopping potential (V s ) is proportional to te frequency of incident radiation.

9 ev s 1 K mv Te value of stopping potential difference is independent of te ligt intensity. Stopping potential (V s ) is proportional to te frequency of incident radiation. Higer te frequency, larger te value of stopping potential, as sown in figure.. Describe Davisson and Germer experiment. Wat did tis experiment conclusively prove? A. Davisson and Germer Experiment: Te wave nature of electron was first explained by Davisson and Germer Experiment. Tey observed diffraction effects wit beams of electrons scattered by crystals. Te experimental arrangement is sown in te figure.it consists of an electron gun wit a tungsten filament F coated wit barium oxide and eated by a low voltage power supply. Electrons emitted by te filament are accelerated to a desired velocity by a suitable ig voltage power supply. Tese are passed troug a cylinder wit fine oles along its axis, to produce a collimated beam. Te electron beam is made to fall on te surface of nickel crystal and are scattered in all directions by te atoms of te crystal. Te intensity of te electron beam scattered in a given direction is measured by te electron detector (collector).te detector can be moved on a circular scale and is connected to a sensitive galvanometer, wic records te current. Te deflection of te galvanometer is proportional to te intensity of te electron beam entering te collector. Te apparatus is enclosed in an evacuated camber.

10 By moving te detector on te circular scale at different positions, te intensity of te scattered electron beam is measured for different values of angle of scattering ( θ ) wic is te angle between te incident and te scattered electron beams. Te variation of intensity (I) of te scattered electron wit te angle of scattering ( θ ) is obtained for different accelerating voltages. For te range of voltages 44V to 68 V, it was noticed tat a strong peak appeared in te intensity (I) of te scattered electron for an accelerating voltage of 54V at a scattering angle θ 5. Te appearance of te peak in a particular direction is due to te constructive interference of electrons scattered from different layers of te regularly spaced atoms of te crystals. Te de-broglie wavelengt ' λ ' associated wit electrons, 1.7. λ nm p V For V 54 volt, λ.167nm From te electron diffraction measurement, te wavelengt of matter waves was found to be.165nm

11 PROBLEMS 1. Find te: (a) Maximum Frequency and (b) Minimum Wavelengt of X-rays produced by 3kV electrons? A. (a) Vmax ev Hz (b) λ c 3 min 18 vmax m.414 nm.. Te work function of cesium metal is.14 ev. Wen ligt of frequency 6 x 14 Hz is incident on te metal surface, potoemission of electrons occurs. Wat is te (a) Maximum kinetic energy of te emitted electrons, (b) Stopping potential and (c) Maximum speed of te emitted potoelectrons? A. Work function of cesium metal φ.14 ev Frequency of ligt υ 6 x 14 Hz (a) Maximum kinetic energy of emitted electrons (Einstein s poto electric equation) KEmax υ φ ( ) J -.14 ev ev.14ev.35 ev (b) Let stopping potential be V. But, KE max ev.35 ev ev V.35 V.

12 (c) Maximum kinetic energy KE max.35 ev 1 mvmax 1 mvmax (Were, v max is te maximum speed and m is te mass of electron) Or Or v max v max km/sec 3. Te potoelectric cut-off voltage in a certain experiment is 1.5 V. Wat is te maximum kinetic energy of potoelectrons emitted? A. V 1.5V K ev ev max o J.4 J 4. Monocromatic ligt of wavelengt 63.8 nm is produced by a elium-neon laser. Te power emitted is 9.4 mw. (a) Find te energy and momentum of eac poton in te ligt beam. (b) How many potons per second, on te average, arrive at a target irradiated by tis beam? (Assume te beam to ave uniform cross-section, wic is less tan te target area). (c) How fast does a ydrogen atom ave to travel in order to ave te same momentum as tat of te poton? A. Wavelengt of monocromatic ligt, λ 63.8 nm 63.8 x -9 m Power 9.4 mw 9.4 x -3 W (a) Energy of eac poton, E c λ x -19 J We know tat momentum of eac poton, p λ

13 (c) Momentum p mv p x -17 kg-m/s Velocity of ydrogen atom, v p 7 m m/s [ m 1.66 x -7 kg (mass of electron)] (b) Let n be te number of potons per second. So, n 3 Power Energy of eac poton x 16 poton/s 3 5. Te energy flux of sunligt reacing te surface of te eart is Wm. How many potons (nearly) per square metre are incident on te Eart per second? Assume tat te potons in te sunligt ave an average wavelengt of 55nm? A. ne Pt P n t E n In an experiment on potoelectric effect, te slope of te cut-off voltage versus frequency 15 of incident ligt is found to be 4.1 Vs. Calculate te value of Planck s constant. V 4.1 Vs, v 15 A. e 1.6 C Planck s constant, V. e v 15 Js 6.59.

14 7. A W sodium lamp radiates energy uniformly in all directions. Te lamp is located at te centre of a large spere tat absorbs all te sodium ligt wic is incident on it. Te wavelengt of te sodium ligt is 589 nm? (a) Wat is te energy per poton associated wit te sodium ligt? (b) At wat rate are te potons delivered to te spere? A. Power of lamp, P W Wavelengt of te sodium ligt, λ 589 nm 589 x -9 m. Planck constant 6.63 x -34 J-s. (a) Energy of eac poton E c λ ( c 3 x 8 m/s) 3.38 x -19 J (b) Let n potons are delivered per second ev.11 ev. n Power Energy of eac poton (From P En) x poton/s 3 x potons/s are delivered Te tresold frequency a certain metal is 3.3 Hz. If ligt of frequency 8. Hz. is incident on te metal, predict te cut of voltage for potoelectric emission. Given Js and e C A. v Hz v Hz V 3.3, 8.,? Maximum K.E. of a potoelectron is ev v v ( v ) v V e ( ) >.3 V.

15 9. Te work function for a certain metal is 4. ev. Will tis metal give potoelectric emission for incident radiation of wavelengt 33 nm? A. Work function φ 4. ev 4. x 1.6 x -19 J 6.7 x -19 J Wavelengt of radiation, λ 33 nm 33 x -9 m If te energy of eac poton is more tan te work function, ten only te potoelectric emission takes place. Energy of eac poton E c 8 λ x -19 J. As te value of energy of eac poton, E 6.7 x -19 J is less tan te work function, φ 6.7 x -19 J. So, no potoelectric emission takes place.. Ligt of frequency 7.1 x 14 Hz is incident on a metal surface. Electrons wit a maximum speed of 6. x 5 m/s are ejected from te surface. Wat is te tresold frequency for potoemission of electrons? A. Frequency of ligt, v 7.1 x 14 Hz Mass of electron, m 9.1 x -31 kg. Maximum speed of electrons, v max 6 x 5 m/s. Let υ be te tresold frequency. Use te formula for kinetic energy KE 1 mv max υ υ i.e., x -34 (υ - υ ) Or v - v x 14 Or v 7.1 x x x 14 Hz. (v 7.1 x 14 Hz)

16 11. Ligt of wavelengt 488nm is produced by an argon laser wic is used in te potoelectric effect. Wen ligt from tis spectral line is incident on te catode, te stopping (cut-off) potential of potoelectrons is.38 V. Find te work function of te material from wic te catode is made? 9 A. λ 488nm 488 m, V.38V From Einstein s potoelectric equation, 1 K mv v W max max Or c ev W λ c W ev λ J Or W J ev Calculate te (a) Momentum and (b) de Broglie wavelengt of te electrons accelerated troug a potential difference of 56 V? A. Potential difference, V 56 V (a) Use te formula for kinetic energy ev 1/ mv ev/m v v ev m Were, m is mass and v is velocity of electron.

17 Momentum associated wit accelerated electron, p mv ev m m evm x -4 kg-m/s. (b) de-broglie wavelengt of electron, λ 1.7 o A 1.7 V x -8 m.164 nm. 13. Wat is te (a) Momentum, (b) Speed and (c) de Broglie Wavelengt of an electron wit kinetic energy of 1 ev? A. Kinetic energy KE 1 ev (a) Momentum, p evm KE.m and e 1.6 x -19 C ( KE ev) x -4 kg-m/s. (b) We know tat momentum p mv or v p/m x 6 m/s. (c) de-broglie wavelengt associated wit electron, 1.7 o 1.7 o λ A A.11 x -9 m.11 nm. V Te wavelengt of ligt from te spectral emission line of sodium is 589 nm. Find te kinetic energy at wic (a) An Electron and (b) A neutron would ave te same de-broglie wavelengt? A. Wavelengt of ligt 589 nm 589 x -9 m Mass of electron m e 9.1 x -31 kg. Mass of neutron m n 1.67 x -7 kg Planck s constant 6.6 x -34 J-s. (a) Using of formula, λ KEm e

18 Kinetic energy of electron, KE e (6.63 ) λ m 9 11 e (589 ) x -5 J. (b) Kinetic energy of neutron KE n (6.63 ) λ m 9 7 n (589 ) x -8 J. 15. Wat is te de-broglie wavelengt of (a) A bullet of mass.4 kg travelling at te speed of 1. km/s (b) A ball of mass.6 kg moving at a speed of 1. m/s and (c) A dust particle of mass 1. x -9 kg drifting wit a speed of. m/s? A. Mass of bullet m.4 kg and speed of bullet v m/s (a) de-broglie wavelengt 6.63 λ mv m.4 kg v 1km/s m/s 1.66 x -35 m. (b) Mass of te ball, m.6 kg and speed of te ball, v 1 m/s 6.63 λ mv x -3 m (c) Mass of a dust particle, m 1-9 kg and speed of te dust particle, v. m/s x -5 m. λ mv 1 9.

19 16. An electron and a poton, eac ave a wavelengt of 1. nm. Find (a) Teir momenta, (b) Te energy of te poton and (c) Te kinetic energy of electron. A. Wavelengt of electron and poton, λ 1 nm -9 m (a) Momentum of electron, 6.63 pe 6.63 x -5 m ( 6.63 x -34 Js) 9 λ Momentum of poton, p x -5 m. λ p 9 (b) Energy of poton, c E 9 λ ev ev 143 ev or E 1.4 kev. (c) Energy of electron, 5 p (6.63 ) E ev 1.51 ev. 31 me (a) For wat kinetic energy of a neutron will te associated de-broglie wavelengt be (b) Also find te de-broglie wavelengt of a neutron, in termal equilibrium wit matter, aving an average kinetic energy of (3/) kt at 3 K. A. (a) de-broglie wavelengt λ 1.4 m Mass of neutron, m n x -7 kg Using te formula, wavelengt associated wit kinetic energy

20 λ m KE Or (6.63 ) KE λ m (1.4 ) n x -1 J. (b) Kinetic energy associated wit temperature x -1 J. 3 KE kt (1.38 ) 3 ( Absolute temperature T 3 K and Boltzmann s constant k 1.38 x -3 J/K) KE 6.1 x -1 J De-Broglie wavelengt associated wit kinetic energy λ m KE λ x - m Sow tat te wavelengt of electromagnetic radiation is equal to te de Broglie wavelengt of its quantum (poton)? A. For a poton, De Broglie wavelengt, λ p For an electromagnetic radiation of frequency v and wavelengt λ ( c v) ' /, Momentum, E v P c c Or c P c λ λ ' Ten, λ ' λ p

21 Tus te wavelengt wavelengt λ of te poton. λ ' of te electromagnetic radiation is te same as te de-broglie 19. Wat is te de-broglie wavelengt of a nitrogen molecule in air at 3K? Assume tat te molecule is moving wit te root-mean-square speed of molecules at tis temperature? 3 1 (Atomic mass of nitrogen v k JK A. Mass of N molecule, 14.76, 1.38 ) m kg kg T 3 K λ 3mKT m m nm

Dual Nature of matter and radiation: m v 1 c

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