• Particle is a material object which is considered as a tiny concentration of matter (localized in space and time) whereas wave is a broad distribution of energy (not localized in space and time).
• The liberation of electrons from any surface of a substance is called electron emission.
• The minimum energy needed for an electron to escape from the metal surface is called work function of that metal.
• 1 eV is equal to 1.602 × (10^-19) J.
• Electric field emission occurs when a very strong electric field is applied across the metal.
• The emission of electrons due to irradiation of light is called photoelectric emission.
• Secondary emission is the process in which electrons are emitted due to the bombardment of fast moving electrons.
• The photoelectric current (i.e. the number of electrons emitted per second) is directly proportional to the intensity of the incident light.
• Stopping potential is that the value of the negative (retarding) potential given to the collecting electrode A which is just sufficient to stop the most energetic photoelectrons emitted and make the photocurrent zero.
• The stopping potential is independent of intensity of the incident light.
• Maximum kinetic energy of the photoelectrons is independent of intensity of the incident light.
• For a given surface, the emission of photoelectrons takes place only if the frequency of incident light is greater than a certain minimum frequency called the threshold frequency.
• According to Planck, a matter is composed of a large number of oscillating particles (atoms) which vibrate with different frequencies.
• According to Einstein, the energy in light is not spread out over wavefronts but is concentrated in small packets or energy quanta.
• The individual light quantum of definite energy and momentum is called photon.
• Light behaves as a wave during its propagation and behaves as a particle during its interaction with matter.
• Photo electric cell or photo cell is a device which converts light energy into electrical energy.
• According to de Broglie hypothesis, all material particles like electrons, protons,neutrons in motion possess wave nature. These waves associated with them are called de Broglie waves or matter waves.
• Wave nature of the electron is used in the construction of electron microscope.
• Louis de Broglie hypothesis of matter waves was experimentally confirmed by Clinton Davisson and Lester Germer in 1927.
• Whenever fast moving electrons fall on the materials, a highly penetrating radiations, namely x-rays, are emitted.
• Continuous x-ray spectrum consists of radiations of all possible wavelengths with a certain minimum wavelength λo .
• Characteristic x-ray spectra show some narrow peaks at some well–defined wavelengths when the target is hit by fast electrons.

I. Multiple Choice Questions

1. The wavelength \(\lambda_{e}\) of an electron and \(\lambda_{\mathrm{p}}\) of a photon of same energy \(E\) are related by (NEET 2013)

a) \(\lambda_{p} \propto \lambda_{e}\)

b) \(\lambda_{p} \propto \sqrt{\lambda_{e}}\)

c) \(\lambda_{p} \propto \frac{1}{\sqrt{\lambda_{e}}}\)

d) \(\lambda_{p} \propto \lambda_{e}^{2}\)

2. In an electron microscope, the electrons are accelerated by a voltage of \(14 \mathrm{kV}\) . If the voltage is changed to \(224 \mathrm{kV}\) , then the de Broglie wavelength associated with the electrons would

a) increase by 2 times

b) decrease by 2 times

c) decrease by 4 times

d) increase by 4 times

3. The wave associated with a moving particle of mass \(3 \times 10^{-6} \mathrm{~g}\) has the same wavelength as an electron moving with a velocity \(6 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}\) . The velocity of the particle is

a) \(1.82 \times 10^{-18} \mathrm{~m} \mathrm{~s}^{-1}\)

b) \(9 \times 10^{-2} \mathrm{~m} \mathrm{~s}^{-1}\)

c) \(3 \times 10^{-31} \mathrm{~m} \mathrm{~s}^{-1}\)

d) \(1.82 \times 10^{-15} \mathrm{~m} \mathrm{~s}^{-1}\)

4. When a metallic surface is illuminated with radiation of wavelength \(\lambda\) , the stopping potential is \(V\) . If the same surface is illuminated with radiation of wavelength \(2 \lambda\) , the stopping potential is \(\frac{V}{4}\) . The threshold wavelength for the metallic surface is (NEET 2016)

a) \(4 \lambda\)

b) \(5 \lambda\)

c) \(\frac{5}{2} \lambda\)

d) \(3 \lambda\)

5. If a light of wavelength \(330 \mathrm{~nm}\) is incident on a metal with work function \(3.55 \mathrm{eV}\) , the electrons are emitted. Then the wavelength of the wave associated with the emitted electron is (Take \(h=6.6 \times 10^{-34} \mathrm{Js}\) )

a) \(<2.75 \times 10^{-9} \mathrm{~m}\)

b) \(\geq 2.75 \times 10^{-9} \mathrm{~m}\)

c) \(\leq 2.75 \times 10^{-12} \mathrm{~m}\)

d) \(<2.5 \times 10^{-10} \mathrm{~m}\)

6. A photoelectric surface is illuminated successively by monochromatic light of wavelength \(\lambda\) and \(\lambda / 2\) . If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the material is (NEET 2015)

a) \(\frac{h c}{\lambda}\)

b) \(\frac{2 h c}{\lambda}\)

c) \(\frac{h c}{3 \lambda}\)

d) \(\frac{h c}{2 \lambda}\)

7. In photoelectric emission, a radiation whose frequency is 4 times threshold frequency of a certain metal is incident on the metal. Then the maximum possible velocity of the emitted electron will be

a) \(\sqrt{\frac{h v_{0}}{m}}\)

b) \(\sqrt{\frac{6 h v_{0}}{m}}\)

c) \(2 \sqrt{\frac{h v_{0}}{m}}\)

d) \(\sqrt{\frac{h v_{0}}{2 m}}\)

8. Two radiations with photon energies \(0.9 \mathrm{eV}\) and \(3.3 \mathrm{eV}\) respectively are falling on a metallic surface successively. If the work function of the metal is \(0.6 \mathrm{eV}\) , then the ratio of maximum speeds of emitted electrons in the two cases will be

a) \(1: 4\)

b) \(1: 3\)

c) \(1: 1\)

d) \(1: 9\)

9. A light source of wavelength \(520 \mathrm{~nm}\) emits \(1.04 \times 10^{15}\) photons per second while the second source of \(460 \mathrm{~nm}\) produces \(1.38 \times 10^{15}\) photons per second. Then the ratio of power of second source to that of first source is

a) 1.00

b) 1.02

c) 1.5

d) 0.98

10. If the mean wavelength of light from sun is taken as \(550 \mathrm{~nm}\) and its mean power as \(3.8 \times 10^{26} \mathrm{~W}\) , then the number of photons emitted per second from the sun is of the order of

a) \(10^{45}\)

b) \(10^{42}\)

c) \(10^{54}\)

d) \(10^{51}\)

11. The threshold wavelength for a metal surface whose photoelectric work function is \(3.313 \mathrm{eV}\) is

a) \(4125 A\)

b) \(3750 A\)

c) \(6000 A\)

d) \(2062.5 A\)

12. A light of wavelength \(500 \mathrm{~nm}\) is incident on a sensitive metal plate of photoelectric work function \(1.235 \mathrm{eV}\) . The kinetic energy of the photo electrons emitted is (Take \(h=6.6 \times 10^{-34} \mathrm{Js}\) )

a) \(0.58 \mathrm{eV}\)

b) \(2.48 \mathrm{eV}\)

c) \(1.24 \mathrm{eV}\)

d) \(1.16 \mathrm{eV}\)

13. Photons of wavelength \(\lambda\) are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius \(R\) by a perpendicular magnetic field having magnitude \(B\) . The work function of the metal is (KVPY-SX 2016)

a) \(\frac{h c}{\lambda}-m_{e}+\frac{e^{2} B^{2} R^{2}}{2 m_{e}}\)

b) \(\frac{h c}{\lambda}+2 m_{e}\left[\frac{e B R}{2 m_{e}}\right]^{2}\)

c) \(\frac{h c}{\lambda}-m_{e} c^{2}-\frac{e^{2} B^{2} R^{2}}{2 m_{e}}\)

d) \(\frac{h c}{\lambda}-2 m_{e}\left[\frac{e B R}{2 m_{e}}\right]^{2}\)

14. The work functions for metals \(A, B\) and \(C\) are \(1.92 \mathrm{eV}, 2.0 \mathrm{eV}\) and \(5.0 \mathrm{eV}\) respectively. The metal/metals which will emit photoelectrons for a radiation of wavelength \(4100 \AA\) is/are

a) A only

b) both \(A\) and \(B\)

c) all these metals

d) none

15. Emission of electrons by the absorption of heat energy is called. .emission.

a) photoelectric

b) field

c) thermionic

d) secondary

Answers

1. d
2. \(\mathrm{c}\)
3. \(d\)
4. \(\mathrm{d}\)
5. b
6. \(\mathrm{d}\)
7. \(\mathrm{b}\)
8. b
9. \(\mathrm{c}\)
10. a \(\begin{array}{lllll}\text { 11. } b & \text { 12. } c & \text { 13. } d & \text { 14.b } & \text { 15. }\end{array}\)

II. Short Answer Questions

1. Why do metals have a large number of free electrons?
2. Define work function of a metal. Give its unit.
3. What is photoelectric effect?
4. How does photocurrent vary with the intensity of the incident light?
5. Give the definition of intensity of light according to quantum concept and its unit.
6. How will you define threshold frequency?
7. What is a photo cell? Mention the different types of photocells.
8. Write the expression for the de Broglie wavelength associated with a charged particle of charge \(q\) and mass \(m\) , when it is accelerated through a potential \(V\) .
9. State de Broglie hypothesis.
10. Why we do not see the wave properties of a baseball?
11. A proton and an electron have same kinetic energy. Which one has greater de Broglie wavelength? Justify.
12. Write the relationship of de Broglie wavelength \(\lambda\) associated with a particle of mass \(m\) in terms of its kinetic energy \(K\) .
13. An electron and an alpha particle have same kinetic energy. How are the de Broglie wavelengths associated with them related?
14. Define stopping potential.
15. What is surface barrier?
16. Mention the two features of \(\mathrm{x}\) -ray spectra, not explained by classical electromagnetic theory.
17. What is Bremsstralung?

III. Long Answer Questions

1. What do you mean by electron emission? Explain briefly various methods of electron emission.
2. Briefly discuss the observations of Hertz, Hallwachs and Lenard.
3. Explain the effect of potential difference on photoelectric current.
4. Explain how frequency of incident light varies with stopping potential.
5. List out the laws of photoelectric effect.
6. Explain why photoelectric effect cannot be explained on the basis of wave nature of light.
7. Give the quantum concept of energy proposed by Max Planck.
8. Obtain Einstein’s photoelectric equation with necessary explanation.
9. Explain experimentally observed facts of photoelectric effect with the help of Einstein’s explanation.
10. Give the construction and working of photo emissive cell.
11. Derive an expression for de Broglie wavelength of electrons.
12. Briefly explain the principle and working of electron microscope.
13. Describe briefly Davisson - Germer experiment which demonstrated the wave nature of electrons.
14. List out the characteristics of photons.
15. Give the applications photocell.
16. How do we obtain characteristic \(x\) -ray spectra?

IV. Numerical problems

1. How many photons per second emanate from a \(50 \mathrm{~mW}\) laser of \(640 \mathrm{~nm}\) ?

2. Calculate the maximum kinetic energy and maximum velocity of the photoelectrons emitted when the stopping potential is \(81 \mathrm{~V}\) for the photoelectric emission experiment.

[Ans: \(1.3 \times 10^{-17} \mathrm{~J} ; 5.3 \times 10^{6} \mathrm{~ms}^{-1}\) ]

3. Calculate the energies of the photons associated with the following radiation:

(i) violet light of \(413 \mathrm{~nm}\) (ii) X-rays of \(0.1 \mathrm{~nm}\) (iii) radio waves of \(10 \mathrm{~m}\) .

[Ans: \(3 \mathrm{eV} ; 12424 \mathrm{eV} ; 1.24 \times 10^{-7} \mathrm{eV}\) ]

4. A \(150 \mathrm{~W}\) lamp emits light of mean wavelength of \(5500 \AA\) . If the efficiency is \(12 \%\) , find out the number of photons emitted by the lamp in one second.

[Ans: \(4.98 \times 10^{19}\) ]

5. How many photons of frequency \(10^{14} \mathrm{~Hz}\) will make up 19.86 J of energy?

[Ans: \(3 \times 10^{20}\) ]

6. What should be the velocity of the electron so that its momentum equals that of \(4000 A\) wavelength photon.

[Ans: \(1818 \mathrm{~ms}^{-1}\) ]

7. When a light of frequency \(9 \times 10^{14} \mathrm{~Hz}\) is incident on a metal surface, photoelectrons are emitted with a maximum speed of \(8 \times 10^{5} \mathrm{~ms}^{-1}\) . Determine the threshold frequency of the surface.

8. When a \(6000 A\) light falls on the cathode of a photo cell, photoemission takes place. If a potential of \(0.8 \mathrm{~V}\) is required to stop emission of electron, then determine the (i) frequency of the light (ii) energy of the incident photon (iii) work function of the cathode material (iv) threshold frequency and (v) net energy of the electron after it leaves the surface.

[Ans: \(5 \times 10^{14} \mathrm{~Hz} ; 2.07 \mathrm{eV} ; 1.27 \mathrm{eV}\) ;

9. A \(3310 \AA\) photon liberates an electron from a material with energy \(3 \times 10^{-19} \mathrm{~J}<span> \( while another \) </span> 5000 A\) photon ejects an electron with energy \(0.972 \times 10^{-19} \mathrm{~J}\) from the same material. Determine the value of Planck’s constant and the threshold wavelength of the material.

10. At the given point of time, the earth receives energy from sun at \(4 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~min}^{-1}\) . Determine the number of photons received on the surface of the Earth per \(\mathrm{cm}^{2}\) per minute. (Given: Mean wavelength of sun light \(=5500 A\) )

[Ans: \(4.65 \times 10^{19}\) ]

11. UV light of wavelength \(1800 A\) is incident on a lithium surface whose threshold wavelength is \(4965 A\) . Determine the maximum energy of the electron emitted.

[Ans: \(4.40 \mathrm{eV}\) ]

12. Calculate the de Broglie wavelength of a proton whose kinetic energy is equal to \(81.9 \times 10^{-15} \mathrm{~J}\) . (Given: mass of proton is 1836 times that of electron).

[Ans: \(4 \times 10^{-14} \mathrm{~m}\) ]

13. A deuteron and an alpha particle are accelerated with the same potential. Which one of the two has i) greater value of de Broglie wavelength associated with it and ii) less kinetic energy? Explain.

[Ans: \(\lambda_{d}=2 \lambda_{\alpha}\) and \(K_{d}=K_{\alpha} / 2\) ]

14. An electron is accelerated through a potential difference of \(81 \mathrm{~V}\) . What is the de Broglie wavelength associated with it? To which part of electromagnetic spectrum does this wavelength correspond?

[Ans: \(\lambda=1.36 A\) and x-rays]

15. The ratio between the de Broglie wavelength associated with proton, accelerated through a potential of \(512 \mathrm{~V}\) and that of alpha particle accelerated through a potential of \(X\) volts is found to be one. Find the value of \(X\) .

[Ans: \(64 \mathrm{~V}]\)

BOOK FOR REFERENCES

1. Arthur Beiser, Shobhit Mahajan, Rai Choudhury, Concepts of Modern Physics, Sixth Edition, McGraw Hill Education (India) Private Limited.
2. H.S. Mani and G.K. Mehta, Introduction to Modern Physics, Affiliated East-West Press Pvt. Ltd.
3. H.C.Verma, Concepts of Physics, Volume 1 and 2, BharathiBhawan publishers.
4. Halliday, Resnick and Walker, Principles of Physics, Wiley publishers.

ICT CORNER

Dual nature of radiation and matter

Topic: Photoelectric effect

In this activity you will be able to visualize how light knocks electrons off a metal target and describe the photoelectric effect experiment.

Steps:

• Open the browser and type “https://phet.colorado.edu/en/simulation/legacy/photoelectric” in the address bar.

• Change intensity of light and observe how the intensity of light will affect the photo electric current and the energy of electrons

• By adjusting the value of wavelength and observe how the wavelength of light will affect the photo electric current and the energy of electrons

• Adjust the value of voltage from the battery and analyse the effect of potential difference on the photoelectric current.

• Change the material of the target and analyse how it will affect the current and the energy of electrons.

• Study the photo electric current – voltage graph and Photo electric current - intensity graph obtained

Note:

Install Java application if it is not in your browser. You can download all the phet simulation and works in off line from https://phet.colorado.edu/en/offline-access.

URL: https://phet.colorado.edu/en/simulation/legacy/photoelectric

• Pictures are indicative only.
• If browser requires, allow Flash Player or Java Script to load the page.