Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

x
x
For better view click here
x
Hire a Tutor
DISCOVER

IIT JEE Physics : Dual Nature

Loading...

Published in: AIEEE | IIT JEE Mains
4,395 Views

Notes for CBSE Physics - Practice problems - Question and answer format

Rahul M / Pune

8 years of teaching experience

Qualification: B.Tech/B.E. (IIT Guwahati - 2009), M.Tech (IIT Guwhahati - 2011), Ph.D (IIT Guwhati - 2016)

Teaches: Chemistry, Mathematics, Physics, AIEEE, Architecture, CET, IIT JEE Mains, NATA Exam, Mechanical, AIPMT, Medical Entrance Exams, NEET

Contact this Tutor
  1. Rahul's Science Academy quartz bulb c PHOTO ELECTRIC EFFECT Class Xll Notes + Problems for self study CBSE/ICSE/MH State Board xaaaaaaaaaaaaaaa CLASS NOTES
  2. Class Notes Read and learn Photo electric Effect The true nature of light is difficult to assess. Experiments showed that light exhibited wavelike properties of diffraction and interference. On the other hand, photoelectric effect indicates that light has the aspects of a particle photon, with both energy and momentum. Thus light exhibits a wave-particle duality. The wave-particle duality was extended to particles as matter waves by Louis de Broglie. His theoretical study on the nature of particles and waves led to the invention of a new mechanics of particles called quantum mechanics. Photoelectric effect Photoelectric emission is the phenomena b me al emit el ctrons under h •nfluence o even isible lig t his e ec was iscovere resonance ele ric I circu s. Hallwachs Experiment which a good number of substances, iefly adiatio such as y ra s, X-rays, ultraviolet and 887 whi e working with Heinri Hertz Quartz bulb It consist of an evac ate quartz bub ith two I c plates at ode nd anode A. h plates are connecte to a battery and ensitive galvanomete . In the absence o an radia 10 incident n the plate , there is low curren and henc there i no deflection In the galvanometer. But, w en an electro magnetic radiation like ultraviolet radiation is allowed 7 c Fig 1 Photo- electric effect to fall on the plate C which is connected to the negative terminal of the battery, a current begins to flow, indicated by the deflection in the galvanometer (G). But, when ultraviolet radiation is made to fall on A, there is no deflection in the galvanometer. These observations reveal that the particles emitted by the plate C due to the photoelectric effect are negatively charged. These particles were found to be electrons. The observed current known as the photoelectric current is due to the flow of electrons. After the study of photoelectric effect by Hallwachs, scientists J.J.Thomson, Lenard, Richardson, Compton did a series of experiments to study the relationship between photoelectric current, intensity of incident radiation, velocity and the kinetic energy of the photo electrons, and their dependence on the wave length of incident radiation used. RahuCs Academy
  3. Read and learn Class Notes Qffect qf intensity Of incident radiation on photo electric current Keeping the frequency of the incident radiation and the potential difference between the cathode and the anode at constant values, the intensity of incident radiation is varied. corresponding photoelectric current is measured in the microammeter. It is found that the photo electric current increases linearly with the intensity of incident radiation (Fig .2). In tensity mg 2 Variation of photoelectric current with intensity of incident radiation. Since the photoelectric current is directly proportional to the number of photoelectrons emitted per second, it implies that the number of photoelectrons emitted per second is proportional to the intensity of incident radiation. Qffect of potential difference on the photoelectric current For a given metallic surface C, keeping the intensity (11) and frequency of the incident radiation constant, the effect of potential difference between the plates on the photoelectric current can be studied. Fig 3 shows the variation of photo electric current with the potential difference V between the two plates. XVhen the positive potential of A is increased, the photoelectric current is also increased. However, if the positive potential is further increæed such that it is large enough to collect all the photo electrons emitted from the plate C, the photoelectric current reaches a certain maximum value and this Photo electric current 13 12 Anode potential UV.J Stopping potential o Retarding potential Fig 3 Variation of photo electric current with potential difference. RahuCs Academy
  4. Class Notes Read and learn current is knoum as saturation current. If the potential of the plate A is made negative, the photocurrent does not mmediately drop to zero but flows in the sarne direction as for positive potential, This shows that the photo electrons are emitted from the plate C finite velocity. If the negative or retarding potential is further increased, the photo current decreases and finally becomes zero at a particular value. Thus, the minirnum negative (retarding) potential given to the anode for which the photo electric current becomes zero is called the cut-off or stopping potential. If m is the of the photo electron emitted with a velocity v then the kinetic enerßy associated unth it is — mv2 2 max • Since at the stopping potential V , the fastest electron is just prevented from reaching the plate A, workdone in bringing the fastest electron to rest kinetic energy of the fastest electron. 1 2 mv 2 The above equation indicates that the stopping potential depends upon the velocity of the fastest electron. The experiment is repeated with the incident radiation of same frequency, but of higher intensities 12 and 13. It is found from the graph, the saturation currents are proportional to the intensities of the radiation, But, the stopping potential remains the same for all the intensities. Thus, for a given frequency of incident stopping potential is independent of its intensity, Ftfect Qf frequency Qf incident radiation potential radiation, 'the on stopping Keeping the photosensitive plate (C) and intensity of incident radiation a constant, the effect of frequency of the incident radiations Photo electric current -V (-VOZ (-vo)a c-voh Retarding potential o Saturation current V.V.J Anode potential Fig 4 Variation of photoelectric current with applied potential difference for different frequency of incident radiation. RahuCs Academy
  5. Read and learn Class Notes on stopping potential is studied. Fig 4 shows the variation of the photo electric current with the applied potential difference V for three different frequencies. From the graph, it is found that higher the frequency of the incident radiation, higher is the value of stopping potential v o. For frequencies vs > v2 > "VI, the corresponding stopping potentials are in the same order (V > (Vo)2 > (Vo)r It is concluded from the graph that, the maximum kinetic Stopping energt of the photoelectrons potential varies linearly with the frequency of incident radiation but is independent of its intensity. If the frequency of the incident radiation is plotted against the corresponding stopping potential, a straight line is obtained as shown in IFig 5. From this graph, it is found that at a frequency vot the value of the o V.V.J Frequency Fig .5 Variation of stopping potential with frequency of incident radiation. stopping potential is zero. This frequency is known the threshold frequency for the photo metal used. The photoelectric effect occums above this frequency and ceases below it. Therefore, threshold frequency is defined the minimum frequency of incident radiation below which the photoelectric emission is not possible completely, however high the intensity of incident radiation may be. The threshold frequency is different for different metals. RahuCs Academy
  6. Read and learn Class Notes Laws Qfphotoetectric emission The experimental observations on photoelectric effect may be summarized as follovcs, which are known as the fundamental laws of photoelectric emission. (i) For a given photo sensitive material, there is a mninimunu frequency called the threshold frequency, below which emission of photoelectrons stops completely, however great the intensity may be. (ii) For a given photosensitive material, the photo electric current is directly proportional to the intensity of the incident radiation, provided the frequency is greater than the threshold frequency. (iii) The photoelectric emission is an instantaneous process. i.e. there is no time lag between the incidence of radiation and the emission of photo electrons. (iv) The maximum kinetic energt of the photo electrons is directly proportional to the frequency of incident radiation, but is independent of its intensity. ight waves and photons Th e ectromagnetic theory of lig ropose by Maxwe I coul ot explai hotoe ec ric effec But, Ma lanck's q antumt eory suc essfully exp ai s photoelectric ef ec heory i ht is emi te in the or o is rete pac et of Accordin t Ian energy calle 'quanta or pho on. Th energy o ach photon = h , where is Planck's constant. Photon is neither a particle nor a wave. In the phenomena like interference, diffraction, polarisation, the photon behaves like a wave. In the phenomena like emission, absorption and interaction with matter (photo electric effect) photon behaves as a particle. Hence light photon has a dual nature. RahuCs Academy
  7. Read and learn Class Notes Einstein's photoelectric equation According to Einstein, the emission of photo electron is the result of the interaction between a single photon of the incident radiation and an electron in the metal. When a photon of energy hv is incident on a metal surface, its energy is used up in two ways : ii A part of the energy of the photon is used in extracting the electron from the surface of metal, since the electrons in the metal are bound to the nucleus. This energy W spent in releasing the photo electron is known as photoelectric work function of the metal. The work function of a photo metal is defined as the minimum amount of energy required to liberate an elect n from the metal surface. he remaining energy of the photon I used to impart kinetic energy to the libera ed e ect n Mathematical form If m is the mæs of an electron and V, its velocity then Energr of the incident photon Work function + Kinetic energr of the electron hv = W + mv2 If the electron does not lose energt by internal collisions, it escapes from the metal, the entire energt (hr-W9 will be exhibited as the knetic energt of the electron. Thus, (he—W9 represents the maximum l
  8. Read and learn Class Notes Verification of Laws of Photoelectric Emission based on Einstein's Photoelectric Equation: i) If v < Yo, then 1/2 mv2 is negative, which is not possible. Therefore,for photoelectric emission to take place v > v o. ii) Since one photon emits one electron, so the number photoelectrons emitted per second is directly proportional to the intensity of incident light. iii) It is clear that 1/2 mv2 v as h and are constant. This shows that K.E. o the photoelectrons is directly proportional to the frequency of the incident light. iv) hotoelectri emission is due to collision between a photon and an electron. As such there can no be ny significant time lag between the incidence of photon and emss•on of hotoelectron. i.e. the process is instantaneous. It is found that delay is onl 10 seconds. Experimental verification QfEinstein's photoelectric equation Einstein's photoelectric equation is, 1 mv2 = v) 2 If Vo is the stopping potential and e, the electronic charge, then 1 ,mv2 = evo 2 From equations (1) and (2), (or) Important.. This is an equation of a straight line. Millikan verified equation (3) experirnentally and found that it is in harmony with the observed fæts. RahuCs Academy
  9. Read and learn Class Notes Variation qf mass with velocity According to Newtonian 'mechanics, the rnæs of a body does not change with velocity. But according to Einstein, the mass of the body changes with velocity. Einstein established the relation befiveen the mæs of a body at rest (me) and the mæs of the same body moving with a velocity v is, 2 1- 2 Example : 'Electrons accelerated in a particle æcelerator, cyclotron with a very high velocity æquire increased mass, exactly as predicted by the above expression. Photoelectric cells and their applications The photoelectri cel is a evice whic convert lght energ into e photo le tric ce Is re of three ypes: i hoto electrica e ergy. emissive el (ii) Pho o voltaic ell and ili Photo conductive cell In this section, a Sim e oto emissiv ell is discussed. It con ists o a highly evacuated bul B made of glas or quartz. semi cylindri a metal plate C connected to the negative terminal of a battery, acts as cathode. This plate is coated with a low work function material such as caesium oxide, in order to get large number of photo mg 6 Photo emissiüe cell electrons. A thin platinum wire A is connected to the positive terminal of the battery and kept along the axis of the metal plate C and this serves as the anode as shown in Fig When a light of suitable wave length falls on the cathode, photo electrons are emitted, which are attracted by the anode A. The resulting current is measured by a micro ammeter. The current produced by this type of cell is proportional to the intensity of the incident light for a given frequency. Applications of photo electric cells Photoelectric cells are used for reproducing sound in cinematography. RahuCs Academy
  10. Class .Notes (iii) (iv) (v) (vi) (vii) (viii) Read and learn They are used for controlling the temperature of furnaces. Photoelectric cells are used for automatic switching on and off the street lights. Photoelectric cells are used in the study of temperature and spectra of stars. Photoelectric cells are also used in obtaining electrical energy from sunlight during space travel. These cells are used in instruments measuring light illumination. These cells are used in opening and closing of door automatically. Photoelectric cells are used in burglar alarm and fire alarm. In burglar alarm, ultraviolet light is continuously made to fall on the photo-cell installed at the door-way. A person entering the door interrupts the beam falling on the photo- cell. The abrupt change in photocurrent is used to start an electric bell ringm . In fire alarm, a number of photo-cells are installed at suitable places in a build ng. e event of breaking out o ire, light radiations fall upon the photoce his om letes the electric circuit hrough an electric bell or a siren which tarts o e atingas w r in signal. RahuCs Academy 10
  11. Read and learn Class Notes Matter waves • The radiant energy has dual aspects of particle and wave, hence a natural question arises, if radiation has a dual nature, why not the matter. In 1924, a French Physicist Louis de Broglie put forward the bold hypothesis that moving particles should possess wave like properties under suitable conditions. He reasoned this idea, from the fact, that nature is symmetrical and hence the basic physical entities — matter and energy should have symmetrical characters. If radiation shows dual aspects, so should matter. de Broglie's wavelength Qf matter waves de Broglie equated the energy equations of Planck (wave) and Einstein (particle). For a wave of frequency v, the energy associated with each photon is given by Planck's relation, where h is Planck's constant. According to Einstein's mæs energr relation, equivalent to enerc, E = mc2 where C is the velocity of light. If, hv = mc2 = mc2 (or) For a particle moving with a velocity v, if c a mæs (since v from equation (3) h h m is c Ymportant where p = mv, the momentum of the particle. These hypothetical matter waves "'Vill have appreciable wavelength only for very light particles. onc us,eon.• i) de Broglie wavelength is inversely proportional to the velocity of the particle. If the particle moves faster, then the wavelength will be smaller and vice versa. RahuCs Academy 11
  12. Read and learn Class Notes ii _lft e particle is at rest, then the de Broglie wavelength is infinite. Such a wave can not be visualized. iii) de Broglie wavelength is inversely proportional to the mass of the particle. The wavelength associated with a heavier particle is smaller than that with a lighter particle. iv) de Broglie wavelength is independent of the charge of the particle. Matter waves, like electromagnetic waves, can travel in vacuum and hence they are not mechanical waves. Matter waves are not electromagnetic waves because they are not produced by accelerated charges. Matter waves are probability waves, amplitude of which gives the probability of existence of the particle at the point. de Broglie wavelength Qf an electron Vy'%en an electron of mass m and charge e is accelerated through a potential difference V, then the energr eVis equal to kinetic energr of the electron. 1 mug = ev (or) v 2 The de Broglie wavelength is h Substituting the value of v, 2eV V.V.J h 2eV h Substituting the known values in equation (2), 12.27 If V = 100 volts, then = 1.227 i.e., the wavelength associated with an electron accelerated by 100 volts is 1.227 A. Since E = ev is kinetic energy* associated jwith the electron, the equation (2) becomes, RahuCs Academy Important 12
  13. Read and learn Class .Notes Previous years sample questions for practice for Answer refer RM notes Rahul Important O CBSE 2011 Define the term stopping potential in relation to photo electric effect. CBSE 2005 Show graphically how the stopping potential for a given photosensitive surface varies with the frequency of the incident radiation. CBS 03 Define photo electric wor unction. How is it related to threshold frequency? CBSE 2013 Write and prove the expression for de Brog/ie's wavelength associated with a charged particle having charge q and mass m, when it is accelerated by a potential V. electron and alpha particl have h sam e Brogll ave/ n th 008 CB associated it them. ow re eir kinet/c energ late t each o er? CBSE 2008 The de Broglie wavelength associated with a proton and a neutron are found to be equal. Which of the two has a higher value of Kinetic energy? CBSE 2006 Define the term threshold frequency and stopping potential in relation to phenomenon of photoelectric effect. How is photoelectric current affected on increasing the a. frequency b. intensity of radiation and why? CBSE 2012 Write Einstein's photoelectric equations. Write clearly how this equation is obtained using the photon picture of electro magnetic relation. Write three silent features observed in photo electric effect, which can be explained using this relation equation. CBSE 2007 Mention the significance of Davison German experiment. An alpha particle and proton are accelerated through the same pd V. Find the ration of the de Broglie wavelengths associated with them. RahuCs Academy 13
  14. Read and learn Class Notes Wave mechanical concept of atom According to de Broglie's an electron of mass m in motion with a velocity v is associated with a wave whose wavelength is given by h where h is Planck's constant. On the basis of de Broglie's hypothesis, an atom model was proposed in which the stationary orbits of Bohr's model were retained. but with the difference that electron in various orbits behaves as a wave. This is shown in Fig It was suggested that stationary orbits are those in which orbital circumference ('hr) is an integral multiple of de Broglie wavelength Fig 7 Wave concept of atom i.e., stationary orbits for an electron are those which contain the complete waves of electron. Thus , 2nr where n = 1, 2, 3 and r is the radius of the circular orbit. Substituting equation (1) in equation (2), h 2Ttr (or) mv r = From equation (3), it is seen that the total angular momentum h of the moving electron is an integral multiple of Thus, de Broglie's concept confirms the Bohr's postulate. RahuCs Academy V.V.J
  15. Rahul Class Notes 1 2 Read and learn Solved Problerns 'The work function of •inc is 6.8 X 10-ag J. Vvhat is the threshold frequency for emission of photoelec&ons from Xnc? Data W = 6.8* 10-19 J v = ? Solution : Work function W = ihv = 6.8 x 10-19 & 8x10—lg & Q6x10—34 v = 1.026 X 1--1m A metallic surface when illuminated with light of wavelength 3833 A emits electrons with energies upto 0.6 ev- Calculate the work function of the metal. a = 3333 A K-E = 0.6 ev . Data Solution : Work function, W = hv or W w 5x10 19 6.626 x 10 10 — kinetic energr - [0.6 *1.6 - 15.96 x 10-19) - ( - 0 96 x 10-191 (Given h = 6.626 x 10- longest wavelength RahuCs Academy -19 1.6x10 = 3.125 Lithium has a work function of 2.3 eV. It is exposed to light of wavelength 4.8 x 10-7 m. Find the maximum kinetic energ with which the elecfron leaves the surface. wmat is the longest wave length which can produce the photo elec&ons? - 1.6 x 10-19 C). Js ; e Data : W = 2.3 eV;h - 6.626 x 10-34 Js ; e = 1.6 x 10-19 C — ? 1, kinetic energ = ? 15
  16. Class Notes Solution . Kinetic But. hv Read and learn energ of ejected electrons = hv — W 6.6263
  17. Class Notes 1. 2. 3. 4. 5. a. b. Read and learn Objective Questions from Previous Years Define intensity of radiation in photon picture of light? [2012] Ans: The intensity of radiation in photo picture of light defined as the photon incident on unit area of a surface in unit time. Show the variation of photocurrent with collector plate potential for different frequencies but same intensity of incident radiation. [2011] Ans. Photo electric rre nt -v (-vn), c-vot Retarding potential o Saturation current Anode potential late pote tial for dif erent pate The varia Ion of otocurre t wit collecto equencles is shown above. The stopping potential in an experiment on photoelectric effect is 1.5V. What is the maximum kinetic energy of the photoelectrons emitted? [2009] Ans: K a cut- f otentia ev The maximum kinetic energy of a photoelectron is 3eV. What is stopping potential? [2009] KEmax = evo So, cut-off potential = 3V. Figure shows variation of stopping potential with the frequency for two photosensitive materials Ml and M2. Why slope is same for both the material? For which material will the emitted electrons have greater kinetic energy for the incident radiation of the same frequency? Justify your answer. 1 Ans. a. Slope of stopping potential with frequency of incident radiation gives the value of plank's constant i.e the reason why the slope is same for both lines. RahuCs Academy 17
  18. Class .Notes Read and learn The intersect of graph on stopping potential gives the value of stopping potential which is higher for M2. So for the photo electrons to be emitted from material M2, KE will also be higher. Metal M2 has higher value of Work function 6. Why photo electric effect cannot be explained on the basis of wave nature of light? Give reasons. 7. Ans. The photo electric effect cannot be explained on the basis of wave number of light because the wave nature of radiations cannot explain the following. a. The instantaneous ejection of photo electrons b. The existence of threshold freque c or a metal surface. h act that kinetic energy of e itted electrons is independent of the intensit of ig ,pmd depends upon its freque cy State three important properties of photos which describe the particle picture of electromagnetic radiations Ans. Th th ee importan properties are a. T ep oton ar mass les as no ec charge nd is sta le hotons are emitted in man natural process c. hotons als that does not spin angu ar mome tu ar frequency. epend n its RahuCs Academy 18
  19. Class Notes Read and learn Davisson and Germer Experiment Davisson and Germer experiment. Experimental arrangement used by Davisson and Germer is as shown in Fig, . Electrons from hot tungsten cathode (C) are accelerated by a potential difference V between the cathode and anode (A). A narrow hole in the anode renders the electrons into a fine beam of Ctygtäl Lattice Nickel Crystal The electrons are scattered in all directions by the atoms in the crystal. 'The intensity of the electron beam scattered in a given direction is found by the use of a detector. By rotating the detector about an axis through the point 0, the intensity of the scattered beam can be measured for different values of 0, the angle between incident and the scattered direction of electron beam. The graph is plotted between angle 0 and the intensity of scattered electron beam. Such graphs are plotted at different accelerating voltages. In each graph, the intensity of electron beam in a given direction is proportional to the distance of the curve from the point 0 (the point of scattering) in that direction. The experimental curves obtained by Davisson and Germer were as shown in Fig. RahuCs Academy m Intensity of scattered beam at 44V Intensity of scattered beam at 4B V From these experimental curves, following inferences can be drawn . (i) (ii) (iii) (v) Intensity of scattered electrons depends upon the angle of scattering Always a 'bumpt or a kink occurs in the curve at (l) = 500, the angle which the scattered beam makes with the incident beam. The size of the bump goes on increasing as the accelerating 'voltage is increased. 'The size of the bump becomes maximum, when accelerating voltage is 54 volt. The size of the bump starts decreasing with further increase in accelerating voltage. However, according to classical physics, there should be very little variation in the intensity of electron beam with the angle of scattering and the accelerating voltage. 19
  20. Read and learn Class Notes Explanation. The selective reflection of the 54 volt electrons at an angle of 500between incident and scattered beam can be termed as the diffraction of electrons from the regularly spaced electrons of nickel crystal by virtue of their wave nature. From Fig. 0 , it follows that 1 = — (1800 o) 2 1 Now, the wave nature of electron and hence the de-Broglie hypothesis will 'be confirmed, if the de-Broglie wavelength of the electrons, when accelerated through 54 volt comes out to be just 1.66 AO. Putting V = 54 then, we get 12.27 = 1.65 A) As the two results are in remarkable agreement, the experiment establishes the wave nature of an electron in particular and of a particle in general For —(1800-500) — - x1300 -650 2 According to Bragg's law, for first order diffraction maximum (n = l). we have 2 d sin x A or 1=2 d sin 0 (2) For nickel crystal, the distance between atomic planes, d 0.91 A) Therefore, = 2 x 0.91 x sin 650 = 1.66 N (3) Now, the wave nature of electron and hence the de-Broglie hypothesis will be confirmed, if the de-Broglie wavelength of the electrons, when accelerated through 54 volt comes out to be just 1.66 N. Rahul's Science Academy CBSE/lCSE/State Board Classes IIT/JEE Entrance Coaching Special Class for NATA and B.Arch Exam RahuCs Academy 20

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related Study Notes

Upload Study Notes

If you have your own Study Notes which you think can benefit others, please upload on LearnPick. For each approved Study Note you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > Study Notes > IIT JEE Physics : Dual Nature