Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter shows that light, long described as a wave, also behaves like a stream of particles, and that particles such as electrons also behave like waves. In this chapter you will study electron emission from metal surfaces and the work function, and the photoelectric effect discovered by Hertz and studied by Hallwachs and Lenard. You will analyse experimental results on how photoelectric current depends on the intensity of light and on the accelerating potential, and how the stopping potential depends on frequency, including the existence of a threshold frequency. You will see why the wave theory of light cannot explain these results, and how Einstein explained them in 1905 by treating light as photons, each of energy hf, giving Einstein's photoelectric equation Kmax = hf - phi0. You will learn the properties of photons. The chapter ends with de Broglie's hypothesis that moving particles have a wavelength lambda = h/p, and you will calculate the de Broglie wavelength of electrons accelerated through a potential difference.

Detailed Worksheet: Dual Nature of Radiation and Matter Section A - Definitions (10 marks) 1. Define work function and threshold frequency of a metal. (2 marks) 2. What is stopping potential? On what does it depend? (2 marks) 3. Write Einstein's photoelectric equation and explain each term. (2 marks) 4. State three properties of photons. (2 marks) 5. State de Broglie's hypothesis and write the expression for the de Broglie wavelength of a particle. (2 marks) Section B - Calculations and Applications (15 marks) 6. Calculate the energy of a photon of wavelength 500 nm in joules and in electron volts (h = 6.63 x 10^-34 J s, c = 3 x 10^8 m/s). (3 marks) 7. The work function of caesium is 2.14 eV. Light of frequency 6.0 x 10^14 Hz falls on it. Find the maximum kinetic energy of the photoelectrons and the stopping potential (h = 4.14 x 10^-15 eV s). (3 marks) 8. The work function of a metal is 2.0 eV. Find its threshold frequency and threshold wavelength (h = 6.63 x 10^-34 J s, e = 1.6 x 10^-19 C). (3 marks) 9. Find the de Broglie wavelength of an electron accelerated from rest through a potential difference of 100 V. (3 marks) 10. A laser emits light of frequency 6.0 x 10^14 Hz with power 2.0 x 10^-3 W. Find the energy of each photon and the number of photons emitted per second. (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled diagram of the experimental arrangement for studying the photoelectric effect, showing the evacuated tube, emitter, collector, window and circuit. (4 marks) 12. Draw graphs of photoelectric current against collector potential for (i) different intensities at the same frequency and (ii) different frequencies at the same intensity. Mark the stopping potentials. (3 marks) 13. Draw a graph of stopping potential against frequency for two metals with different work functions. Show what the slope and intercepts represent. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. In a photoelectric experiment, the stopping potential is 0.47 V for light of frequency 6.0 x 10^14 Hz and 1.30 V for light of frequency 8.0 x 10^14 Hz. Calculate Planck's constant and the work function of the metal (e = 1.6 x 10^-19 C). (5 marks) 15. Calculate the de Broglie wavelength of (i) an electron moving at 5.4 x 10^6 m/s and (ii) a ball of mass 0.12 kg moving at 20 m/s (m of electron = 9.11 x 10^-31 kg). Explain why wave nature is noticed for the electron but not for the ball. (5 marks) 16. Explain three features of the photoelectric effect that the wave theory of light cannot explain, and show how Einstein's photon picture explains each of them. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use the given constants and show units. Draw neat, labelled graphs.