2018 H2 Quantum Physics Tutorial (Teachers)

9749 H2 PHYSICS Tutorial Nanyang Junior College 1 Chapter 19 QUANTUM PHYSICS speed of light in free space c = 3.00 × 108 m s-1 elementary charge e = 1.60 × 10-19 C the Planck constant h = 6.63 × 10-34 Js unified atomic mass constant u = 1.66 × 10-27 kg rest mass of electron me = 9.11 × 10-31 kg rest mass of proton mp = 1.67 × 10-27 kg Self-Attempt Questions Photoelectric Effect 1 What provides evidence for the particulate nature of electromagnetic radiation? A Electrons can be diffracted by a carbon film. B Light can be diffracted by an obstacle. C Light from two coherent sources can produce an interference pattern. D Photoelectric emission occurs only for incident frequencies above a minimum value. 2 The figure below shows a setup used to investigate the photoelectric effect. When radiation of wavelength 225 nm is incident on the emitter, photoelectrons are emitted and a photocurrent is registered by the ammeter. Which of the following statements is true? A If the polarity of the p.d. source is switched around, photoelectrons will not be emitted anymore. B If radiation of a shorter wavelength is used, the ammeter will register a higher photocurrent. C If radiation of a longer wavelength is used, the ammeter will register a higher photocurrent. D If the intensity of the radiation is increased, the ammeter will register a higher photocurrent. A emitter collector incident radiation p.d. source

9749 H2 PHYSICS Tutorial Nanyang Junior College 2 Changing the wavelength of the radiation changes the KEmax of the electrons, it does not change the rate of emission of photoelectrons. Switching the polarity of the p.d. source will not prevent the emission of photoelectrons as long as the radiation is above the threshold frequency. Increase the intensity of radiation will increase the current as the rate of emission of photoelectrons will increase. 3 In a particular photoelectric experiment, it was found that when light of wavelength 187 nm is incident on the metal surface, the stopping potential is 2.70 V. What will be the stopping potential if light of wavelength 87 nm is used instead? A 1.70 V B 4.94 V C 10.3 V D No electrons will be emitted ( ) ( ) ( ) ( )( ) 8 34 19 9 19 3.0 10 6.63 10 1.6 10 2.7 187 10 6.32 10 J S ch eV φλ φ φ −− − − = + × × = +× × = × When wavelength is changed to 87 nm, ( )( ) ( ) ( ) 8 34 19 19 9 3.0 10 6.63 10 6.32 10 1.6 10 87 10 10.3 V S S V V − −− − × × = × +× × = 4 In a photoelectric emission experiment using light of a certain frequency, the maximum kinetic energy Ek of the emitted photoelectrons is measured. Which graph represents the way in which Ek depends on the intensity I of the light? A B C D In photoelectric effect, kinetic energy Ek is independent of the intensity I of light. Line Spectra 5 Which one of the following provides direct evidence for the existence of discrete energy levels in an atom? I Ek 0 I Ek 0 I Ek 0 I Ek 0

9749 H2 PHYSICS Tutorial Nanyang Junior College 3 A The continuous spectrum of the light emitted by a white-hot metal. B The emission of photoelectrons from a metal. C The ionisation of gas atoms when bombarded by alpha particles. D The line emission spectrum of a gas at low pressure. 6 Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in order of increasing magnitude λ1, λ2 and λ3. Which of the following equations correctly relates λ1, λ2 and λ3? Since 123λλλ<< Then 123fff>> and 123EEE>> . 123EEE= + 123 hc hc hc λλλ= + 123 111 λλλ= + 7 The diagram shows the electron energy levels, referred to the ground state (lowest possible energy) as zero, for four different isolated atoms. Which atom can produce radiation of the shortest wavelength when atoms in the ground state are bombarded with electrons of energy W? A B C D A B C D 321 111 λλλ += 231 111 λλλ −= 321 111 λλλ −= 1 23λλλ= + E1 E3 E2 w

9749 H2 PHYSICS Tutorial Nanyang Junior College 4 Shortest wavelength, implies maximum energy difference since E1-E2 = hf. Since all ground level energies are the same, the largest energy difference between any 2 levels less then W will be B. 8 Some of the energy levels of the hydrogen atoms are shown. How many maximum possible spectral emission lines can be observed if photons each of energy 12.85 eV are incident onto the hydrogen atoms that are initial at ground state? A 0 B 3 C 6 D 10 9 The diagram illustrates four transitions between three discrete energy levels of an isolated atom. Which transition produces the line of longest wavelength in the absorption spectrum of a gas of these atoms? X-Rays 10 In the figure below, graph P shows an X-ray spectrum from an X-ray tube. -13.6 eV -3.39 eV -1.51 eV -0.85 eV -0.54 eV E A B C D

9749 H2 PHYSICS Tutorial Nanyang Junior College 5 What are the possible changes that can be made to obtain graph Q? A Change the target metal. B Increase the filament current of the cathode. C Reduce the distance between the cathode and the target. D Increase the potential difference between the cathode and target. Wave – Particle Duality 11 What is the de Broglie wavelength of a particle of mass, m and kinetic energy, E? A h mE B 2h mE C 2h mE D 2 h mE 12 A beam of electrons is incident on a crystal lattice. The regularly spaced parallel planes of ions in the lattice can serve as a diffraction grating. The spacing between each plane is 1 x 10-8 m. In order for significant diffraction to occur, the kinetic energy of the each electron should be of the order of A 10-2 eV B 10-21 eV C 10-26 eV D 10-34 eV 13 A proton has a kinetic energy of 1.00 MeV. If its momentum is measured with an uncertainty of 1.00 %, what is the minimum uncertainty in its position? A 1.15 × 10-21 m C 1.23 × 10-10 m B 2.87 × 10-12 m D 1.24 × 108 m ∆p = 0.01 p and p = (2m KE)1/2 (using KE = ½ mv2 and p = mv) hence ∆p ∆x = h implies 12 27 6 19 2.87 10 0.01 2 1.67 10 1.0 10 1.6 10 m− −− ∆= = × ×× × ×××× hx

9749 H2 PHYSICS Tutorial Nanyang Junior College 6 Discussion Questions Photoelectric Effect 1 Electromagnetic radiation is incident normally on the surface of a metal. Electrons are emitted from the surface and these are attracted to a positively charged electrode, as shown in Fig. 1.1. Fig 1.1 (a) Name the effect which gives rise to the emission of the electrons. The photoelectric effect (b) State a word equation, based on the principle of conservation of energy, which describes this effect. The energy of the incident photon is equal to the sum of the work function energy of the metal surface and the maximum kinetic energy of the emitted photoelectrons (c) (i) The current recorded on the microammeter is 2.1 μA. Calculate the number of electrons emitted per second from the surface. 𝐼𝐼 = 𝑄𝑄𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑡𝑡 = 𝑁𝑁𝑒𝑒𝑒𝑒 𝑡𝑡 ∴ 𝑁𝑁𝑒𝑒 𝑡𝑡 = 𝐼𝐼 𝑒𝑒 = 2.1 × 10−6 1.6 × 10−19 = 1.3 × 1013 (ii) The incident radiation has wavelength 240 nm. Calculate the energy of a photon incident on the surface. 𝐸𝐸 = ℎ𝑐𝑐 𝜆𝜆 = (6.63 × 10−34)(3.0 × 108) (240 × 10−9) = 8.3 × 10−19 J variable d.c. supply µA X V metal EM radiation

9749 H2 PHYSICS Tutorial Nanyang Junior College 7 (d) The intensity of the incident radiation is 8.2 x 10 3 W m-2 and the area of the surface is 2.0 cm2. (i) Calculate the power of the radiation incident on the surface. 𝑃𝑃 = 𝐼𝐼𝐼𝐼𝑡𝑡𝑒𝑒𝐼