Physics · Textbook solutions

Dual Nature of Radiation and Matter

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 32 questions

14. Dual Nature of Radiation and Matter — worked examples

6 q

Solved Examples

Worked · 6
  1. Solved Ex.14.1
    Radiation of intensity 0.5×10−40.5 \times 10^{-4} W/m2^2 falls on the emitter in a photoelectric set-up. The emitter (cathode) is made up of potassium and has an area of 5 cm2^2. Let us assume that the electrons from only the surface are knocked off by the radiation. According to the wave theory, what will be the time required to notice some deflection in the microammeter connected in the circuit? (Given the metallic radius of potassium atom is 230 pm and work function of potassium is 2.3 eV.)
  2. Solved Ex.14.2
    (a) Calculate the energies of photons corresponding to ultraviolet light and red light, given that their wavelengths are 3000 A˚\mathring{A} and 7000 A˚\mathring{A} respectively. (Remember that the photon are not coloured. Colour is human perception for that frequency range.) (b) A typical FM radio station has its broadcast frequency 98.3 MHz. What is the energy of an FM photon of this frequency?
  3. Solved Ex.14.3
    The wavelength and power of the incident light is 4000 A˚\mathring{A} and 0.1 W respectively. What is the minimum change in the energy of the incident light? What is the number of incident photons?
  4. Solved Ex.14.4
    An electron is accelerated through a potential of 120 V. Find its de Broglie wavelength.
  5. Solved Ex.14.5
    A student, weighing 45 kg, is running with a speed of 8 km per hr on a foot path 2 m wide. A small car, weighing 1200 kg, is moving with a speed of 60 km per hr on a 20 m wide road. Calculate their de Broglie wavelengths.
  6. Solved Ex.14.6
    Calculate the de Broglie wavelength of an electron moving with kinetic energy of 100 eV passing through a circular hole of diameter 2 A˚\mathring{A}.

Exercises

26 q

Choose the correct answer

Practice · 5
  1. Choose the correct answer.
    Ex Q.1 (i)
    A photocell is used to automatically switch on the street lights in the evening when the sunlight is low in intensity. Thus it has to work with visible light. The material of the cathode of the photo cell is
    1. A.
      zinc
    2. B.
      aluminum
    3. C.
      nickel
    4. D.
      potassium
  2. Ex Q.1 (ii)
    Polychromatic (containing many different frequencies) radiation is used in an experiment on photoelectric effect. The stopping potential
    1. A.
      will depend on the average wavelength
    2. B.
      will depend on the longest wavelength
    3. C.
      will depend on the shortest wavelength
    4. D.
      does not depend on the wavelength
  3. Ex Q.1 (iii)
    An electron, a proton, an α\alpha-particle and a hydrogen atom are moving with the same kinetic energy. The associated de Broglie wavelength will be longest for
    1. A.
      electron
    2. B.
      proton
    3. C.
      α\alpha-particle
    4. D.
      hydrogen atom
  4. Ex Q.1 (iv)
    If NRedN_{Red} and NBlueN_{Blue} are the number of photons emitted by the respective sources of equal power and equal dimensions in unit time, then
    1. A.
      NRed<NBlueN_{Red} < N_{Blue}
    2. B.
      NRed=NBlueN_{Red} = N_{Blue}
    3. C.
      NRed>NBlueN_{Red} > N_{Blue}
    4. D.
      NRed≈NBlueN_{Red} \approx N_{Blue}
  5. Ex Q.1 (v)
    The equation E=pcE = pc is valid
    1. A.
      for all sub-atomic particles
    2. B.
      is valid for an electron but not for a photon
    3. C.
      is valid for a photon but not for an electron
    4. D.
      is valid for both an electron and a photon

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    What is photoelectric effect?
  2. Ex Q.2 (ii)
    Can microwaves be used in the experiment on photoelectric effect?
  3. Ex Q.2 (iii)
    Is it always possible to see photoelectric effect with red light?
  4. Ex Q.2 (iv)
    Using the values of work function given in Table 14.1, tell which metal will require the highest frequency of incident radiation to generate photocurrent. Table 14.1 : Typical values of work function for some common metals.
    MetalWork function (in eV)
    Potassium2.3
    Sodium2.4
    Calcium2.9
    Zinc3.6
    Silver4.3
    Aluminum4.3
    Tungsten4.5
    Copper4.7
    Nickel5.0
    Gold5.1
  5. Ex Q.2 (v)
    What do you understand by the term wave-particle duality? Where does it apply?

Solve the following

Practice · 16
  1. Ex Q.3
    Explain the inverse linear dependence of stopping potential on the incident wavelength in a photoelectric effect experiment.
  2. Ex Q.4
    It is observed in an experiment on photoelectric effect that an increase in the intensity of the incident radiation does not change the maximum kinetic energy of the electrons. Where does the extra energy of the incident radiation go? Is it lost? State your answer with explanatory reasoning.
  3. Ex Q.5
    Explain what do you understand by the de Broglie wavelength of an electron. Will an electron at rest have an associated de Broglie wavelength? Justify your answer.
  4. Ex Q.6
    State the importance of Davisson and Germer experiment.
  5. Ex Q.7
    What will be the energy of each photon in monochromatic light of frequency 5×10145 \times 10^{14} Hz?
  6. Ex Q.8
    Observations from an experiment on photoelectric effect for the stopping potential by varying the incident frequency were plotted. The slope of the linear curve was found to be approximately 4.1×10−154.1 \times 10^{-15} V s. Given that the charge of an electron is 1.6×10−191.6 \times 10^{-19} C, find the value of the Planck's constant hh.
  7. Ex Q.9
    The threshold wavelength of tungsten is 2.76×10−52.76 \times 10^{-5} cm. (a) Explain why no photoelectrons are emitted when the wavelength is more than 2.76×10−52.76 \times 10^{-5} cm. (b) What will be the maximum kinetic energy of electrons ejected in each of the following cases (i) if ultraviolet radiation of wavelength λ=1.80×10−5\lambda = 1.80 \times 10^{-5} cm and (ii) radiation of frequency 4×10154 \times 10^{15} Hz is made incident on the tungsten surface.
  8. Ex Q.10
    Photocurrent recorded in the micro ammeter in an experimental set-up of photoelectric effect vanishes when the retarding potential is more than 0.8 V if the wavelength of incident radiation is 4950 A˚\mathring{A}. If the source of incident radiation is changed, the stopping potential turns out to be 1.2 V. Find the work function of the cathode material and the wavelength of the second source.
  9. Ex Q.11
    Radiation of wavelength 4500 A˚\mathring{A} is incident on a metal having work function 2.0 eV. Due to the presence of a magnetic field B, the most energetic photoelectrons emitted in a direction perpendicular to the field move along a circular path of radius 20 cm. What is the value of the magnetic field B?
  10. Ex Q.12
    Given the following data for incident wavelength and the stopping potential obtained from an experiment on photoelectric effect, estimate the value of Planck's constant and the work function of the cathode material. What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?
    Incident wavelength (in A˚\mathring{A})25363650
    Stopping potential (in V)1.950.5
  11. Ex Q.13
    Calculate the wavelength associated with an electron, its momentum and speed (a) when it is accelerated through a potential of 54 V, (b) when it is moving with kinetic energy of 150 eV.
  12. Ex Q.14
    The de Broglie wavelengths associated with an electron and a proton are same. What will be the ratio of (i) their momenta (ii) their kinetic energies?
  13. Ex Q.15
    Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an α\alpha-particle, what are the possibilities for the other particle?
  14. Ex Q.16
    What is the speed of a proton having de Broglie wavelength of 0.08 A˚\mathring{A}?
  15. Ex Q.17
    In nuclear reactors, neutrons travel with energies of 5×10−215 \times 10^{-21} J. Find their speed and wavelength.
  16. Ex Q.18
    Find the ratio of the de Broglie wavelengths of an electron and a proton when both are moving with the (a) same speed, (b) same energy and (c) same momentum? State which of the two will have the longer wavelength in each case?