NYJC_EJC 2026 Quantum Physics Tutorial

9814 H3 Physics (2026) Quantum Physics Tutorial 1 Particulate nature of photon 1 (a) Describe the nature of a γ-ray photon. (b) When a beam of γ-rays or X-rays passes through matter, it may interact with an electron and be scattered through an angle θ, as show in Fig. 1.1. Fig. 1.1 According to a theory, the energy E ’ of the scattered radiation is given by 2 11 1 ' (1 cos ) eEE mc θ−−= , where E is the energy of the incident radiation, me is the mass of the electron and c is the speed of light. The electron, originally at rest, recoils in a direction defined by the angle φ. (i) A 60 Co source emits γ-ray of energy 1.33 MeV. 1. Find the largest possible energy loss this γ-ray can suffer in an interaction with a stationary electron. 2. In what direction does the recoil electron move after this interaction? [6] (ii) The reduction in energy of the γ-radiation can be detected as a change in wavelength. 1. Is this wavelength change an increase or a decrease? 2. Show that the magnitude ∆λ of the wavelength change corresponding to the energy reduction (E − E’ ) is given by ∆λ = A(1− cos θ ), where A is a constant. Find A in terms of m e, c and the Planck constant h. [5] incident radiation scattered radiation recoil electron θ φ

9814 H3 Physics (2026) Quantum Physics Tutorial 2 (iii) In an experiment to measure ∆ λ for X -rays of incident wavelength 7.09 ×10−11 m, scattered from graphite at various angles θ , the following results were obtained: θ / ° 45 75 90 120 135 ∆λ / 10−11 m 0.07 0.17 0.23 0.35 0.41 Each of the readings of θ was subjected to an uncertainty of ± 1°, and each of the value of ∆λ values to an uncertainty of ± 0.01×10−11 m. By plotting a suitable linear graph using graph paper, investigate the extent to which these results support the theoretical relationship. State your conclusion. [7] [Special Paper Nov 1994 Q9] Photoelectric effect 2 An evacuated tube contains two parallel metal electrodes, one of which is an emitter of electrons and the other a collector. When the emitter is illuminated with electromagnetic radiation of photon energy 4.7 eV at a power of 3.8 mW, photoelectrons are emitted. The potential difference V between collector and emitter is adjusted, and the photocurrent I is measured. Fig. 2.1 is a graph of the variation with V of I. Fig. 2.1 (i) Calculate the rate at which photons are incident on the emitter. [2] (ii) Calculate the maximum rate at which electrons leave the emitter. [1] (iii) Explain the difference between your answers in (i) and (ii). [2] (iv) Calculate the maximum speed at which electrons leave the emitter. [3] I / 10−8A − 0.5 0 V / V 0.5 1.0 0.8 A B

9814 H3 Physics (2026) Quantum Physics Tutorial 3 (v) Determine the work function of the material of the emitter. [1] (