__Dual Nature of Radiation and Matter__

__Dual Nature of Radiation and Matter__

**[1 Mark Questions]**

1. Define the intensity of radiation on the basis of the photon picture of light. Write its SI unit.

2. The graph shows the variation of * stopping potential* with the frequency of incident radiation for two photosensitive metals A and B. Which one of the two has a higher value of work-function? Justify your answer

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3. In the photoelectric effect, why should the photoelectric current increases as the intensity of the monochromatic radiation incident on a photosensitive surface be increased? Explain.

4. The given graph shows the variation of photoelectric current (I) versus applied voltage (V) for two different photosensitive materials and for two different intensities of the incident radiation. Identify pairs of curves that correspond to different materials but same intensity radiation.

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

6. Define the term stopping potential in relation to the __photoelectric effect__.

7. Show the variation of photocurrent with collector plate potential for different frequencies but the same intensity of incident radiation.

8. Show the variation of photocurrent with collector plate potential for different intensities but the same frequency of incident radiation.

9. The stopping potential in an experiment on the photoelectric effect is 1.5 V. What is the maximum kinetic energy of the photoelectrons emitted?

10. The maximum kinetic energy of a photoelectron is 3 eV. What is its stopping potential?

11. The stopping potential in an experiment on photoelectric effect is 2 V.What is the maximum kinetic energy of the photoelectrons emitted?

12. The figure shows a plot of three curves a, b, c showing the variation of photocurrent vs. collector plate potential for three different intensitiesI1, I2 and I3 having frequencies Ï…1, Ï…2 and Ï…3 respectively incident on photosensitive surface.

Point out the two curves for which the incident radiations have the same frequency but different intensities.

13. Write the expression for the **de-Broglie wavelength** associated with a charged particle having charge *q* and mass *m*, when it is accelerated by a potential difference.

14. State __de Broglie's hypothesis__.

15. A proton and an electron have same kinetic energy. Which one has greater de Broglie's wavelength and why?

16. Write a relationship of de-Broglie wavelength Î» associated with a particle of mass m in terms of its kinetic energy.

17. Show graphically, the variation of de-Broglie wavelength (Î») with the potential (V) through which an electron is accelerated from rest.

18. Name an experiment, which shows wave nature of the electron. Which phenomenon was observed in this experiment using an electron beam?

19. An electron and Î± â€“ particle have same kinetic energy. How is the de-Broglie wavelengths associated with them related?

20. Draw a plot, showing the variation of photoelectric current versus the intensity of incident radiation on a given photosensitive surface.

**[2 Mark Questions]**

1. Monochromatic light of frequency 6.0 x 1014 Hz is produced by a laser. The power emitted is 2.0 x 103 W. Estimate the number of photons emitted per second on an average by the source.

2. Write three basic properties of photons which are used to obtain Einsteinâ€™s photoelectric equation. Use this equation to draw a plot of the maximum kinetic energy of the electrons emitted versus the frequency of incident radiation.

3. Answer the following questions.

a. Define the term stopping potential.

b. Plot a graph showing the variation of photoelectric current as a function of anode potential for two light beams of same intensity but of different frequencies Ï…1 and Ï…2(Ï…1<Ï…2).

4. Answer the following questions.

a. Define the term threshold frequency as used in the photoelectric effect.

b. 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).

5. Two monochromatic radiations of frequenciesÏ…1 and Ï…2(Ï…1>Ï…2)and having the same intensity are in turn, incident on a photosensitive surface to cause photoelectric emission. Explain giving a reason in which case,

a. more number of electrons will be emitted.

b. the maximum kinetic energy of the emitted photoelectrons will be more.

6. Write Einsteinâ€™s photoelectric equation. State clearly the three salient features observed in the photoelectric effect which can be explained on the basis of the above equation.

7. Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions WÂ1 and W2(W1 and W2). On what factors does the a. Do slope and intercept of the lines depend?

8. Write Einsteinâ€™s photoelectric equation relating the maximum kinetic energy of the emitted electron to the frequency of the radiation incident on a photosensitive surface. State clearly the basic elementary process involved in the photoelectric effect.

9. Write Einsteinâ€™s photoelectric equation. Explain the terms:

a. Threshold frequency and b. Stopping potential.

10. Write Einsteinâ€™s photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation. Write the three salient features observed in the photoelectric effect which can be explained using this equation.

11. Define the terms (i) â€˜cut-off voltageâ€™ and (ii) â€˜threshold frequencyâ€™ in relation to the phenomenon of the photoelectric effect. Using Einsteinâ€™s photoelectric equations how the cut-off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot/graph.

12. Write Einsteinâ€™s photoelectric equation in terms of the stopping potential and the threshold frequency for a given photosensitive material. Draw a plot showing the variation of stopping potential versus the frequency of incident radiation.

13. A proton and a deuteron are accelerated through the same accelerating potential. Which one of the two has

a) The greater value of de-Broglie wavelength associated with it and b) Less momentum?

Give reasons to justify your answer.

14. A deuteron and anÎ±-particle are accelerated with the same accelerating potential. Which one of the two has

a)The greater value of de-Broglie wavelength, associated with it and

b) Less kinetic energy? Explain.

15. X-rays fall on a photosensitive surface to cause photoelectric emission. Assuming that the work function of the surface can be neglected, find the relation between the de-Broglie wavelength (Î») of the electrons emitted to the energy (EÏ…) of the incident photons. The draw of the graph for Î» as function of EÏ….

16. An electron is revolving around the nucleus with a constant speed of 2.2 x 108 m/s. Find the de-Broglie wavelength associated with it.

17. AnÎ±-particle and a proton are accelerated from rest by the same potential. Find the ratio of their de-Broglie wavelength.

18. An electron is associated through a potential difference of 100 V. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?

19. Find the ratio of de-Broglie wavelengths associated with a. Protons accelerated through a potential of 128 V and b. Î±-particles accelerated through a potential of 64 V.

20. Derive an expression for the de-Broglie wavelength associated with an electron accelerated through a potential V. Draw a schematic diagram of a localized wave describing the wave nature of the moving electron.

21. In Davisson- Germerexperiment, state the observations which led to

a. Show the wave nature of electrons and b. Confirm the de-Broglie relation.

22. For what kinetic energy of a neutron will the associated de-Broglie wavelength be 1.32 x 10-10 m?

**[3 Mark Questions]**

1. Answer the following questions.

a. Why the photoelectric effect cannot be explained on the basis of the wave nature of light? Give reasons.

b. Write the basic features of the photon picture of electromagnetic radiation on which Einsteinâ€™s photoelectric equation is based.

2. Write Einsteinâ€™s photoelectric equation and point out any two characteristic properties of photons on which this equation is based. Briefly explain three observed features which can be explained by this equation.

3. Answer the following questions.

a. State three important properties of photons which describe the particle picture of electromagnetic radiation.

b. Use Einsteinâ€™s photoelectric equation to define the terms:

i. Stopping potential and

ii. Threshold frequency.

4. Write two characteristic features observed in the photoelectric effect that support the photon picture of electromagnetic radiation. Draw a graph between the frequency of incident radiation (*v*) and the maximum kinetic energy of the electrons emitted from the surface of a photosensitive material. State clearly how this graph can be used to determine

a. Planckâ€™s constant and b. The work function of the material.

5. Write Einsteinâ€™s photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation. Write the three salient features observed in the photoelectric effect which can be explained using this equation.

6. Draw a plot showing the variation of photoelectric current with collector plate potential for two different frequencies, Ï…2>Ï…1of incident radiation having the same intensity. In which case will the stopping potential be higher? Justify your answer.

7. An electron microscope uses electrons accelerated by a voltage of 50kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture, etc. to be the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?

8. Answer the following questions.

a. Describe briefly how the Davisson-Germerexperiment demonstrated the wave nature of electrons.

b. An electron is accelerated from rest through a potential V, obtain the expression for the de-Broglie wavelength associated with it.

9. An electron and a photon each have a wavelength of 1 nm. Find

a. Their momenta

b. The energy of the photon and

The kinetic energy of the electron.

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