PYQ Vault

Physics · Textbook solutions

Dual Nature of Radiation and Matter

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 14 questions

Worked Examples

3 q

Solved Examples

Worked · 3
  1. Eg 11.1
    Monochromatic light of frequency 6.0×1014 Hz6.0 \times 10^{14}\,\text{Hz} is produced by a laser. The power emitted is 2.0×10−3 W2.0 \times 10^{-3}\,\text{W}. (a) What is the energy of a photon in the light beam? (b) How many photons per second, on an average, are emitted by the source?
  2. Eg 11.2
    The work function of caesium is 2.14 eV2.14\,\text{eV}. Find (a) the threshold frequency for caesium, and (b) the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.60 V0.60\,\text{V}.
  3. Eg 11.3
    What is the de Broglie wavelength associated with (a) an electron moving with a speed of 5.4×106 m/s5.4 \times 10^{6}\,\text{m/s}, and (b) a ball of mass 150 g150\,\text{g} travelling at 30.0 m/s30.0\,\text{m/s}?

Exercises

11 q
  1. Ex 11.1
    Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV30\,\text{kV} electrons.
  2. Ex 11.2
    The work function of caesium metal is 2.14 eV2.14\,\text{eV}. When light of frequency 6×1014 Hz6 \times 10^{14}\,\text{Hz} is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) Stopping potential, and (c) maximum speed of the emitted photoelectrons?
  3. Ex 11.3
    The photoelectric cut-off voltage in a certain experiment is 1.5 V1.5\,\text{V}. What is the maximum kinetic energy of photoelectrons emitted?
  4. Ex 11.4
    Monochromatic light of wavelength 632.8 nm632.8\,\text{nm} is produced by a helium-neon laser. The power emitted is 9.42 mW9.42\,\text{mW}. (a) Find the energy and momentum of each photon in the light beam, (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
  5. Ex 11.5
    In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be 4.12×10−15 V s4.12 \times 10^{-15}\,\text{V s}. Calculate the value of Planck's constant.
  6. Ex 11.6
    The threshold frequency for a certain metal is 3.3×1014 Hz3.3 \times 10^{14}\,\text{Hz}. If light of frequency 8.2×1014 Hz8.2 \times 10^{14}\,\text{Hz} is incident on the metal, predict the cut-off voltage for the photoelectric emission.
  7. Ex 11.7
    The work function for a certain metal is 4.2 eV4.2\,\text{eV}. Will this metal give hotoelectric emission for incident radiation of wavelength 330 nm330\,\text{nm}?
  8. Ex 11.8
    Light of frequency 7.21×1014 Hz7.21 \times 10^{14}\,\text{Hz} is incident on a metal surface. Electrons with a maximum speed of 6.0×105 m/s6.0 \times 10^{5}\,\text{m/s} are ejected from the surface. What is the threshold frequency for photoemission of electrons?
  9. Ex 11.9
    Light of wavelength 488 nm488\,\text{nm} is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V0.38\,\text{V}. Find the work function of the material from which the emitter is made.
  10. Ex 11.10
    What is the de Broglie wavelength of (a) a bullet of mass 0.040 kg0.040\,\text{kg} travelling at the speed of 1.0 km/s1.0\,\text{km/s}, (b) a ball of mass 0.060 kg0.060\,\text{kg} moving at a speed of 1.0 m/s1.0\,\text{m/s}, and (c) a dust particle of mass 1.0×10−9 kg1.0 \times 10^{-9}\,\text{kg} drifting with a speed of 2.2 m/s2.2\,\text{m/s}?
  11. Ex 11.11
    Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).