TE Enriched Sample (E)

The quantum theory of light Enrichment 27 1.2 In a photoelectric emission experiment, monochromatic light of different frequencies is shone on a metal surface. The corresponding stopping potentials V s are plotted against the frequencies f as shown. (a) What is the maximum KE of the photoelectrons when the monochromatic light has a frequency of 1.2 × 10 15 Hz? (b) Show that the equation of the line is V e hf e s z = - where h is the Planck constant, e is the electron charge, and z is the work function of the metal surface. What do the slope, the y -intercept and the x -intercept of the V s – f graph represent? (c) Find the slope of the graph and estimate the Planck constant. (Given: e = 1.60 × 10 - 19 C) (d) What are the threshold frequency and work function of the metal? (e) On the same graph, sketch the V s – f graph that would be obtained for a metal with a smaller work function. Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Stopping potential at this frequency = 3 V Max. KE of a photoelectron eV . J eV 3 4 80 10 19 s # = = = - Analysing a V s – f graph Example 1.5 f / 10 14 Hz 1 4 8 12 0 2 3 V s / V Another evidence for the particle nature of light suggests that the light beam consists of a stream of tiny particles, i.e. photons. Today, we can obtain such images of photons using powerful digital cameras. The figures below show a set of double-slit interference of light with decreasing brightness (from left to right). We say light behaves as a wave because it undergoes interference. Bright and dark fringes appear when a beam of light shines on a screen through a double-slit. However, strange things happen if we greatly reduce the intensity of the beam. When the beam is extremely faint, little dots appear on the screen one by one. This Teaching notes Remind Ss that • it is eV s that gives the max. KE, not the voltage V s alone. • when describing HOW to measure the max. KE, one has to state both the condition (no photocurrent) and the procedure to achieve it (adjust the voltage). (See DSE 2018 Q2a) ( MC: DSE 2012 Q2.4, 2015 Q2.3, 2021 Q2.4) ( SQ: DSE 2018 Q2, 2022 Q2) Teaching notes Ss need to get familiar with variations of this graph, e.g. V s ➞ K max , and f ➞ hf or 1/ λ or λ , especially the physical meanings and dependency of their slopes and intercepts (see DSE 2021 Q2.4, 2022 Q2b). Sample © United Prime Educational Publishing (HK) Limited, Pearson Education Asia Limited 2023 All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publishers.