Bihar Board - Class 12 Physics - Chapter 11: Dual Nature of Radiation and Matter Short Answer Question

1. What is the photoelectric effect? What are photoelectrons?

Answer: The phenomenon of emission of electrons from the surface of a metal, when radiation of a frequency equal to or greater than the threshold frequency for that metal is incident on it, is called photoelectric effect. The electrons so ejected are called photoelectrons.

2. Define the term 'photoelectric work function' of a metal.

Answer: Photoelectric work function of a metal is the minimum amount of energy required to just eject an electron from the surface of a metal.

3. Define the term 'stopping potential' in relation to photoelectric effect.

Answer: The least value of negative (retarding) potential given to the collector plate with respect to the photosensitive emitter plate so as to stop even the fastest moving photoelectron from reaching the collector plate is called the stopping potential. Thus, at stopping potential, photoelectric current becomes zero. Stopping potential (V0) is a measure of maximum kinetic energy of the photoelectrons. In fact,

eV0 = Kmax

4. How does the 'stopping potential' in Photoelectric emission depend upon: (a) the intensity of the incident radiation in a photocell, and (b) the frequency of incident radiation?

Answer:

• (a) The stopping potential for a given photosensitive material is independent of the intensity of the incident radiation.

• (b) For frequencies greater than threshold frequency of a photosensitive material, the stopping potential linearly increases with increase in frequency of incident radiation.

5. Briefly explain the term 'threshold frequency for a photosensitive metal'.

Answer: Threshold frequency (v0) for a given photosensitive metal is that minimum frequency for the metal below which no photoelectric emission is possible, no matter how intense the radiation may be or for how long it is incident on the surface.

Value of threshold frequency varies from metal to metal and is correlated to the work function 0 of the metal as per relation

0=hv0.

6. For a given photosensitive material and with a source of constant frequency (v > v0) of incident radiation, how does the photocurrent vary with the intensity of incident light?

Answer: For a given photosensitive material and with a source of constant frequency v, which is greater than the threshold frequency, the value of saturation photocurrent is directly proportional to intensity of light and increases linearly with increase in intensity of incident light.

7. Is photoelectric emission from the surface of a given metal possible at all frequencies/ wavelengths? 

Answer: No, photoelectron emission is not possible for all frequencies/wavelengths of incident radiation on a metal surface. For causing photoelectric emission, the energy of incident radiation photons must be at least equal to the work function of the given metal.

8. Do nonmetals show photoelectric effect? Why?

Answer: No, nonmetals do not ordinarily show photoelectric effect because they do not have free (conduction) electrons. Nonmetals have only bound electrons, which cannot be ejected easily.

9. How does the maximum kinetic energy of electrons emitted from a metal vary with its work function?

Answer: For radiation of a given high frequency incident on a metal surface, the maximum kinetic energy of emitted photoelectrons is less if the work function of metal is high and vice versa. It is in accordance with Einstein's photoelectric equation hv = 0 + Kmax

10. A neutron and an α-particle have the same momenta. Which has a higher wavelength? Give a reason. Given that the mass of an α-particle is four times the mass of a neutron.

Answer: Since neutrons and α-particles have the same value of momenta p, hence their de Broglie wavelengths (λ = h/p) are exactly equal.

11. If the intensity of the incident radiation in a photocell is increased, how does the stopping potential vary?

Answer: The value of stopping potential remains unchanged because stopping potential does not depend on the intensity of the incident radiation.

12. Why are alkali metals the most suited for photoelectric emission?

Answer: Atoms of alkali metals have only one electron in the valence orbit, which can be easily made free. So, the work function of alkali metals is very small. Therefore, alkali metals can cause photoelectric emission for even visible light and are, thus, the most suited for photoelectric emission.

13. Two monochromatic radiations, blue and violet, of the same intensity, are incident on a photosensitive surface and cause photoelectric emission. Would: (a) the number of electrons emitted per second, and (b) the maximum kinetic energy of the electrons, be equal in the two cases. 

Answer: 

• (a) As intensity of both radiations, blue and violet, is same, hence the number of electrons emitted per second from the surface will be exactly equal for both radiations. It is because the number of photoelectrons ejected per unit time depends on intensity of incident light but is independent of its frequency.

• (b) The maximum kinetic energy of ejected photoelectrons increases linearly with increase in frequency of incident light and frequency of violet light is more than that of blue light. Hence, maximum kinetic energy of ejected electrons is more for violet light.

14. Red light, however bright it is, cannot cause the emission of photoelectrons from a clean zinc surface. However, even weak ultraviolet radiation can do so. Why?

Answer: Threshold frequency of zinc lies in the ultraviolet region because the work function of zinc is comparatively large. Consequently, red light, whose frequency is less than the threshold frequency, cannot cause photoelectron emission from a zinc surface. Ultraviolet radiation of frequencies greater than threshold frequency can cause emission of photoelectrons irrespective of its intensity.

15. Electrons are emitted by a photosensitive surface when it is illuminated by green light but no emission takes place by yellow light. Will the electrons be emitted when the surface is illuminated by (a) red light, and (b) blue light?

Answer: We know that for constituent colors of white light, the frequency gradually increases from red side to blue-violet side. As the given photosensitive material allows electron emission for green light but not for yellow light, the threshold frequency lies in the green region.

• (a) As the frequency of red light is even less than that of yellow light, no photoelectric emission is possible with red light.

• (b) As the frequency of blue light is even greater than that of green light, photoelectric emission will definitely take place for blue light.

16. Every metal has a definite work function. If incident radiation is monochromatic, then why do all the photoelectrons not come out with the same energy?

Answer: Because of the energy distribution of free electrons in a metal, the energy required to eject an electron from the metal surface is different for different electrons. Work function of a metal is the least energy required by an electron to come out of the metal. Thus, although incident light is monochromatic (of same frequency and hence energy), the ejected photoelectrons have different values of kinetic energy.

17. Is it essential that each incident photon on a photosensitive metal surface should eject a photoelectron? Explain in brief.

Answer: The number of photoelectrons being emitted by a metal surface is proportional to the intensity of light (or the number of incident photons) but we cannot claim that each incident photon will cause ejection of a photoelectron. An electron is ejected when an incident photon is absorbed by a stationary free electron such that energy provided by the photon is absorbed by a stationary free electron so that energy provided by the photon is sufficient to eject the electron. As absorption of a photon by an electron in metal is a statistical phenomenon, we are not sure about the emission of electrons for each incident photon.

18. Define the term ‘stopping potential’ in relation to photoelectric effect. 

Answer: The value of the retarding potential at which the photoelectric current becomes zero is called the cut off or stopping potential for the given frequency of the incident radiation.

19. Show on a plot the nature of variation of photoelectric current with the intensity of radiation incident on a photosensitive surface. 

Answer:

20. A source of light of frequency greater than the threshold frequency is placed at a distance of 1 m from the emitter plate of a photoelectric cell. The stopping potential is found to be V. If the distance of the light source from the emitter is reduced, explain giving reason, what change will you observe in the (a) photoelectric current, and (b) stopping potential.

Answer: When the source of light is brought closer to the emitter plate of a photoelectric cell, the frequency of light remains unchanged but intensity of light incident on the emitter plate increases in accordance with inverse square law. As a result:

• (a) the number of photoelectrons ejected per unit time and consequently, the photoelectric current increases.

• (b) the maximum energy of ejected photoelectrons and hence, the value of stopping potential remains unchanged.

21. In Davisson and Germer's experiment, state the observations which led to: (a) show the wave nature of electrons, and (b) confirm the de Broglie relation.

Answer: 

(a) In Davisson and Germer's experiment, it was observed that electrons are diffracted by crystals. As only a wave can exhibit diffraction, it shows that moving electrons behave as waves.

(b) While studying the variation of the intensity of the scattered electrons with angle of scattering, Davisson and Germer observed a sharp peak for a certain angle. It was on account of constructive interference of electrons scattered from different layers of lattice of the crystal. From the electron diffraction experiment, the wavelength of electron waves was measured, which was found to be in an excellent agreement with de Broglie's theoretical value. Thus, the experiment confirmed the de Broglie relation.

22. State de-Broglie hypothesis. 

Answer:

According to de-Broglie hypothesis, a particle of mass on moving with given velocity v must be associated with a matter waiver of wavelength X given by:

                                               =hp=hmv

23. If the distance between the source of light and the cathode of a photocell is doubled, how does it affect the stopping potential applied to the photocell? 

Answer:

Stopping potential remains unchanged, if the distance between the light source and cathode is doubled.

24. An electron is accelerated through a potential difference of 64 volts. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond? 

Answer:

According to de-Broglie wavelength,

                =1.227Vnm=1.22764=1.2278=0.1533 nm

This wavelength is associated with X-rays.

25. (i) Define the term ‘threshold frequency’ as used in photoelectric effect.

(ii) Plot a graph showing the variation of photoelectric current as a function of anode potential for two light beams having the same frequency but different intensities I1 and I2 (I1 > I2). 

Answer:

(i) Threshold frequency. The minimum frequency V0 which the incident light must possess so as to eject photoelectrons from a metal surface, is called threshold frequency of the metal.

(ii)