LONG-ANSWERS QUESTIONS

LONG-ANSWERS QUESTIONS 1. What are de Broglie waves? Show that the de Broglie wavelength associated with an electron, accelerated through V volts, is given by 12.3 A o λ= V (AISSCE 1992) 2. Discuss Davissson and Germer experiment to verify de Broglie waves. (AISSCE 2003) 3. What is photoelectric effect? Write Einstein s photoelectric equation. How this equation explains the various laws of photoelectric effect? or Explain the laws of photoelectric emission on the basis of Einstein s photoelectric equation. (AISSCE 1998) ANSWERS 1. Dual nature of matter. De Broglie Waves. de Broglie suggested that like radiation, matter also has dual nature. That is, with every material particle a wave is associated. This wave is called matter wave or de Broglie wave. If a particle of mass m is moving with a speed v, then the wavelength of the matter wave associated with it is given by h λ= mv If a particle of mass m and charge q is accelerated through a p.d. V, then

Therefore, v = 2qV m h λ = 2 mq For an electron, this yields λ = 1 V 10 34 6.625 10 1 31 19 2 9.1 10 1.6 10 12.3 10 = V m 12.3 o or λ= A V 2. Davisson and Germer Experiment : The existence of de Broglie waves for electron was experimentally verified by Davisson and Germer by using diffraction method similar to that employed by Bragg for X-rays because the de Broglie wavelength of electrons is of the same order of magnitude as the X-rays wavelengths. V

Incident Beam (a) Electron Gun Detector The experimental arrangement is shown in Fig. 7.4 (a). Davisson and Germer directed an electron beam against a (111) face of a crystal of nickel. The smallest separation between nickel atoms is d = 0.91 A o. The intensity of the scattered electrons was measured as a function of the latitude angle φ measured from the axis of the incident electron beam for different electron energies. Fig 7.4 (b) shows the graph for 54 ev electron beam. It was found that the beam has a diffraction peak at φ = 50 o. The corresponding angle (θ) of incidence and scattering relative to the Bragg planes is given by θ + φ + θ = 180 o = 50 0 54V (b) 180 φ 180 50 or θ= = = 65 2 2 According to Bragg s law for first order diffraction maximum, we have λ = 2d sin θ

= 2 0.91 sin 65 o = 1.65 A o Now, according to de Broglie hypothesis 12.3 12.3 λ= A = = 1.66 A V 54 The close agreement between the two values demonstrates the correctness of the de Broglie hypothesis. 3. Photoelectric effect : Emission of electrons from the surface of a metal when electromagnetic radiation of high enough frequency falls on it is called the photoelectric effect. Emitting Plate A Radiation e Evacuated Tube Collecting Plate The apparatus is as shown. When the collecting plate is given high enough potential V, all the emitted electrons reach the collecting plate and the photoelectric current will saturate. Main Features (Laws) of Photoelectric Emission: (1) No electrons are emitted if the incident radiation has a frequency less than a threshold value ν 0. The value of ν 0 varies from metal to metal. V

(2) The kinetic energy of the emitted electrons varies from zero to a maximum value. The maximum value of energy depends on the frequency and not on the intensity of radiation. It varies linearly with the frequency. (3) The number of photoelectrons emitted per second, i.e., the photoelectric current, is proportional to the intensity of radiation. (4) The photoelectric emission is an instantaneous process, i.e., there is negligible time lag between the incidence of radiation and the emission of electrons. Failure of classical physics. These results cannot be explained if we consider e.m.radiation to be wave-like, because in that case the maximum energy of emitted electrons should depend on the intensity and not on the frequencyof radiation. Elinstein s Theory. Photons. Einstein explained the photoelectric effect using Planck s quantum hypothesis. According to this theory, the incident radiation consists of tiny bundles of energy called quanta or photons. If the frequency of the radiation is ν, then the photon has energy hν, where h is Planck s constant, having value 6.625 10-34 Js. When a photon collides with an electron, it is absorbed, imparting all its energy to the electron instantaneously. If the work function of the metal is W, then the maximum energy E max, and the corresponding velocity v max, of the emitted electron are given by 1 2 Emax = mv max = hν W 2 This is called Einstein s Photoelectric equation, showing that E max depends linearly on ν. The threshold frequency ν 0 is obviously given by hν 0 = W Therefore, E max = h (ν ν 0 )

Clearly, no emission is possible if ν < ν 0 An increase in the intensity of radiation results in an increase in the number of photons striking per second but not in the energy of individual photons.therefore, the photoelectric current increases but not the energy of emitted electrons. Lastly, since the electron emission is the result of a direct collision between an electron and a photon, there is no time delay before emission starts.

VERY SHORT AND SHORT-ANSWERS QUESTIONS 1. The wavelength of electromagnetic radiation is doubled. What will happen to the energy of photons? (AISSCE Delhi 1993) 2. On what factor(s) does the energy carried by a photon of light depend. 3. What is the magnitude of the fundamental charge? 4. What is photoelectric effect? (AISSCE Delhi 1992) 5. A proton and an electron have the same de Broglie wavelength. Which of them moves faster and which possesses more kinetic energy. (Sample Paper 1992) 6. Draw a graph to show the variation of stopping potential with the frequency of radiation incident on a metal plate. How can the value of Planck s constant be determined by this graph? (AISSCE 1995) 7. What is photoelectric effect? Explain the effect of increase of (i) frequency (ii) intensity of incident radiations on the photoelectrons emitted by a photo tube. (AISSCE 1994) 8. Name one physical process for the release of electrons from the surface of a metal. (AISSCE 1990) 9. What is the rest mass of photon? (AISSCE Delhi 1990) 10. Light from a bulb falls on a wooden table but no photoelectrons are emitted. Why? (AISSCE 1997) 11. Name a phenomenon which cannot be explained assuming wave nature of light. 12. Does each incident photon eject a photoelectron? 13. Two metals A and B have work functions 2eV and 4eV, respectively. Which metal has a lower threshold wavelength for photoelectric effect? (AISSCE 1996) 14. Can photoelectric effect be explained on the basis of wave nature of light?

15. What determines the cut off potential for photelectrons? 16. If the intensity of incident radiation on a metal surface is doubled, what happens to the kinetic energy of emitted electrons? (AISSCE 1993) 17. Write the energy (E) of a photon in term of its frequency (ν). 18. What is the effect on the velocity of the emitted photoelectrons if the wavelength of the incident light is decreased? 19. Do nonmetals show photoelectric effect? 20. It is harder to remove a free electron from copper than from sodium. Which metal has greater work function? 21. Write an expression for the de Broglie wavelength associated with an electron accelerated through a potential difference V. 22. What are the main features (Laws) of photoelectric emission? 23. Define work function of a material and write an expression for it in terms of the threshold frequency of photoelectric emission. 24. Wrtie the energy (E) of a photon in terms of wevelength (λ). 25. Do all photoelectrons emitted from a metal surface have the same kinetic energy? 26. Does the stopping potential depend on the frequency of incident light? 27. Define threshold frequency. 28. What are the different methods used for electron emission from a metal surface? 29. Define threshold wavelength? 30. The threshold wavelength for a metal surface is λ 0. How is it related to the work function of the metal?

ANSWERS hc 1. Energy of a photon is given by E = hν =. So, when the wavelength (λ) is doubled, energy λ (E) will become half. 2. Energy of a photon depends on its frequency. 3. 1.6 10 19 C. 4. The phenomenon of emission of electrons when radiation of suitable frequency strikes a metallic surface is called photoelectric effect. 5. de Broglie wavelength is given by h λ= mv h or mv = λ Since λ is same for both, we have m p v p = m e v e (where e stands for electron and p for proton) but m e < m p. So v e > v p 1 2 me v E e e 2 ( me ve) ve ve Now = = = E 1 p 2 m ( mp vp) vp vp p vp 2 Since v e > v p, therefore E e > E p.

6. The graph is shown in Fig. 7.1. The slope of this graph, on multiplying with the electronic change e, gives the value of Planck s constant, as can be seen form the photoelectric equation: h W E = ev0 = hν W V0 = ν e e 7. Photoelectric effect : See Q. 4. (a) If the frequency of incident photons is increased, the kinetic energy of ejected Fig. 7.1 photoelectrons will increase. (b) With the increase in the intensity of incident radiation, number of photoelectrons emitted increases and so the photoelectric current increases. 8. Photoelectric effect. 9. Zero. 10. The work function of wood is much higher than the energy of a photon emitted from the bulb. Hence photoelectric emission is not possible. 11. Photoelectric effect. 12. No. some of the incident photons may be absorbed in some other way by the metal surface. hc 13. Work function W = hν 0 = λ 0 hc Threshold wavelength λ 0 = W Thus, B has lower threshold wavelength.

14. No. 15. The frequency of incident photons determines the cut-off potential. 16. The kinetic energy of emitted electrons remains the same as it does not depend on the intensity of incident radiation. 17. E = hν, where h is Planck s constant. 18. If the wavelength of incident light is decreased, the energy of light increases and hence the velocity of emitted electrons increases. 19. Yes, but with electromagnetic radiations of much higher frequencies compared to metals. 20. Copper. h 21. λ=. 2 evm 22. Main Features (Laws) of Photoelectric Emission : (1) No electrons are emitted if the incident radiation has a frequency less than a threshold value ν 0. The value of ν 0 varies from metal to metal. (2) The kinetic energy of the emitted electrons varies from zero to a maximum value. The maximum value of energy depends on the frequency and not on the intensity of radiation. It varies linearly with the frequency. (3) The number of photoelectrons emitted per second, i.e., the photoelectric current, is proportional to the intensity of radiation. (4) The photoelectric emission is an instantaneous process, i.e., there is negligible time lag between the incidence of radiation and the emission of electrons. 23. The minimum energy required to remove one electron from the surface of a material is called the work function of that material.

If ν 0 is the threshold frequency for photoelectric emission from a metal, then the work function of that is given by W = hν 0. 24. E = hc / λ, where h is Planck s constant. 25. No. 26. Yes, with increase in the frequency of incident light, the stopping potential also increases as V 0 = (h / e) ν (W/e) 27. Threshold Frequency is the minimum frequency of incident radiation required for photoelectric emission from a metal. 28. Different methods of electron emission from a metal surface are : (1) Thermionic emission (2) Photoelectric emission (3) Field emission 29. If the wavelength of light incident on a metal is greater than a certain value, no photoelectrons are emitted from the metal. This maximum wavelength is called threshold wavelength. 30. hc W = λ 0

VERY SHORT AND SHORT-ANSWERS QUESTIONS 31. The work function of aluminium is 4.2 ev. If two photons, each of energy 3.0 ev, strike the aluminium surface, will the emission of electron be possible? 32. If the frequency of light falling on a metal plate is doubled, will the maximum kinetic energy of the emitted photoelectrons be doubled? 33. The work function of metal A is greater than that of metal B. Which of the two metals has greater threshold frequency for photoelectric emission? 34. Out of visible, microwave and ultraviolet, which radiation is most suitable for photoelectric emission from Zn surface? 35. Green light can eject electrons from a photosensitive surface while orange light cannot. Will blue and red lights eject electrons from the same surface? 36. Photoelectrons have energies varying from zero to a maximum value, even when the incident light is monochromatic. Why? 37. What information is derived from electron diffraction experiments? 38. What is the value of stopping potential in a photocell if the maximum kinetic energy of emitted electrons is 7 ev? 39. Derive an expression for the velocity acquired by an electron when it is accelerated through a potential difference V. 40. What is a photocell? 41. Mention some applications of photocells. 42. What is Einstein s photoelectric equation? 43. Define cut-off (stopping) potential. 44. Calculate the threshold frequency for a metal whose work function is 0.1 ev. 45. Which cell is used for the reproduction of sound in cinema. 46. What are de Broglie (or matter) waves?

47. Write an expression for the de Broglie wavelength associated with a particle of mass m moving with velocity v. 48. For a given frequency, plot a graph between photoelectric current and intensity of incident light. 49. Show graphically the variation of de Broglie wavelength with the momentum of a particle. 50. What is the momentum of a photon of frequency ν? 51. Which nature of light, particle or wave, is established by photoelectric effect? 52. Which has larger de Broglie wavelength, a proton or an electron, when both are moving with the same speed? 53. An electron and a proton are possessing the same amount of kinetic energy. Which of the two has larger de Broglie wavelength? 54. Why are alkali metals most suitable for photoelectric emission? 55. Define electron-volt and obtain its value in joule. 56. An electron is accelerated through a potential of 1 kv. Calculate the gain in its energy in (i) ev (ii) joule. 57. Why is wave nature of matter not significant for macroscopic bodies? 58. Name a phenomenon which illustrates the particle nature of light. (AISSCE 1992C) 59. Two metals A and B have work functions 2.3 ev and 4.0 ev respectively. Which of these metals will be more suitable for photoelectric cell working with visible light? 60. What is the effect on the maximum velocity of photoelectrons if the wavelength of incident radiation is decreased? 61. What is the relation between momentum and de Broglie wavelength for a particle? 62. Are matter waves electromagnetic? 63. What is the use of photocell in cinematography? 64. For a given kinetic energy arrange the following in order of increasing de Broglie wavelength: electron, proton and α-particle.

65. Define the terms threshold frequency and stopping potential for photoelectric effect. Show graphically how the stopping potential for a given metal varies with frequency of the incident radiation. Mark threshold frequency on this graph. (AISSCE 1998) 66. If the frequency of the incident radiation on the cathode of a photocell is doubled, how will the following change : (i) Kinetic energy of the electrons, (ii) Photoelectric current, (iii) Stopping potential. Justify your answer. (AISSCE Delhi 1999) 67. State the dependence of work function on the kinetic energy of electrons emitted in a photocell. If the intensity of incident radiation is doubled, what changes occur in the stopping potential and the photoelectric current. (AISSCE Delhi 2000) 68. How deos (i) photoelectric current (ii) kinetic energy of photoelectrons emitted in a photocell vary if the intensity of the incident radiation is doubled? (AISSCE 2000) ANSWERS 31. No, at a time one photon strikes one electron and the emission of electron is possible only if the energy of each incident photon is more than the work function of the metal. 32. No, since the kinetic energy of the emitted photon is given by, E = hν W 33. The threshold frequency is greater for A. 34. Ultraviolet. 35. Blue light will eject electrons since its frequency is higher than that of green light but red light will not eject electrons because its frequency is less than that of orange light.

36. It is because all the electrons are not emitted from the surface of the metal. The energy of incident photon is constant but the energies used up by different electrons to free themselves from the metal are different. 37. Electron diffraction experiments establish the wave nature of matter. 38. We have ev 0 = E max or ev 0 = 7 1.6 10 19 or V 0 = 7 V 39. Since the electron gains kinetic energy at the expense of electrical potential energy, we have 1 2 2 mv = ev ev or v = m 2 ev or v = m 40. A photocell is a device which makes use of the photoelectric effect to convert a change in the intensity of illumination into a change in electric current. 41. Applications of Photocells (a) They are used in burglar alarms. (b) They are used to measure the intensity of light in meteorology and scientific work. (c) They are used for the reproduction of sound. (d) They are used in street lights for automatic switch on and off. (e) They are used to open the doors automatically. 2 2

42. Einstein s Photoelectric Equation : The maximum kinetic energy of emitted photoelectrons from a metal surface is given by Emax = hν W = h( ν ν0 ), where ν is the freqency of incident photon, W is the work function of the metal and ν 0 is the thereshold frequency. 43. Cut-off potential is the negative potential that must be applied to the collecting plate to make the photoelectric current zero. 44. We have W = h ν 0 19 W 0.1 1.6 10 or ν 0 = = 34 h 6.6 10 13 = 2.4 10 Hz 45. Photoemissive cell. 46. According to de Broglie, with each particle a wave of suitable wavelength is associated. These waves are called de Broglie (or matter) waves. 47. h λ= mv

48. 49. Fig. 7.2 Fig. 7.3

50. Momentum of a photon 51. Particle nature of light. E hν p = =. c c h 52. λ=. For the same speed we have mv λp me = λ m e p Since m < m, so λ >λ. e p e p 1 λ m 53. In terms of kinetic energy, de Broglie wavelength is given by h λ = 2 me So λ = h/ 2 m E e λ = h/ 2m E p e p λ m e p = λp me Since m p > m e so λ e > λ p i.e., de Broglie wavelength for electron is larger. 54. Alkali metals are most suitable for photoelectric emission because they have the lowest values of work function. 55. One electron-volt is the energy gained by an electron when it is accelerated through a potential difference of one volt. 1 electron-volt (ev) = 1.6 10 19 C 1 V = 1.6 10 19 J.

56. (i) 1 ke V (ii) 1000 1.6 10 19 = 1.6 10 16 J. 57. de Broglie wavelength h 1 λ= λ mv m For a macroscopic object mass is so large that the resulting debroglie wavelength is too small to be observed. 58. Photoelectric effect. 59. Metal A will be more suitable, because its work function is lower. 60. Einstein s photo electric equation is 1 2 hν= W + mvmax 2 hc 1 2 or = W + mvmax λ 2 where W is the work function of the metal. Clearly, if the wavelength of incident radiation is decreased, the velocity of photoelectrons will increase. h 61. λ= p 62. No, matter waves are not electromagnetic. 63. In reproduction of sound from sound tracks. 64. h λ= 2 me 1 m

Now, m α > m p > m e λ α < λ p < λ e Thus the required order is electron, proton, α-particle. 65. See Qs. 27, 43 and 6. 66. (i) The kinetic energy of photoelectrons is given by E max = hν W Clearly, if ν is doubled, E max will be more than doubled because the work function (W) of the metal is fixed. (ii) The photoelectric current does not change on increasing the frequency of radiation. This is because whatever be the energy (hν) of an incident photon, it can eject only one electron. (iii) The stopping potential is given by Emax V0 =. e With the increase in the frequency of radiation, E max increases and hence V 0 increases. 67. Wrok function is a property of the target materal. It is related to the energy of the emitted electron as E = hν W. If the intensity of incident radiation is doubled, the stopping potential remains the same but the photoelectric current is doubled. 68. See above answer.