DHS 19 Quantum Physics (Tutorial Solutions)

DHS Physics H2 Year 6 / 2025 Topic 19 Quantum Physics Tutorial Suggested Answers 1 For Internal Use Only 21-May-25 Photoelectric Effect 1. Estimate the rate of emission of photons emitted by a 4.00 mW red laser (632 nm). 3 9 16 1 34 8 4.00 10 632 10 1.27 10 s6.63 10 3.00 10 Nhf NhcP t t N P t hc                  2. Light of wavelength 3.82 × 10−7 m is incident on a substance and electrons are emitted with a maximum speed of 6.87 × 105 m s −1. Calculate the work function1 energy of the substance. [N07 H2 P3 Q7c] Using Einstein’s photoelectric equation,   max max 34 8 31 5 2 7 19 6.63 10 3.00 10 1 9.11 10 (6.87 10 )23.82 10 3.06 10 J hf KE hc KE                     3 When light of wavelength 350 nm falls on a potassium surface, electrons are emitted that have a maximum kinetic energy of 1.31 e V. Determine (a) the work function of potassium, (b) the cut-off wavelength, (c) the frequency corresponding to the cut-off wavelength. (a) Using Einstein’s photoelectric equation,   34 8 19 19 max max 9 6.63 10 3.00 10 1.31 1.60 10 3.59 10 J 350 10 hc hc KE KE                          (b) At cut-off wavelength c , KEmax = 0 34 8 9 19 6.63 10 3.00 10 554 10 m 554 nm 3.59 10 c c hc hc                (c) Threshold frequency 8 14 9 3.00 10 5.42 10 Hz 554 10 c c cf        1 There are conduction electrons in a metal which are not attached to a particular atom. Removing thes e electrons from a metal surface using a photon involves a different amount of energy from that for ionizing a single metal atom. Thus, the work function energy of a metal differs from the energy required to remove the outer electron from an isolated atom. There is a simple connection between the work function energy Φ of a solid metal and the first ionization energy (Ei)1 of its corresponding gaseous atoms: Φ ~ ½(Ei)1.

DHS Physics H2 Year 6 / 2025 Topic 19 Quantum Physics Tutorial Suggested Answers 2 For Internal Use Only 21-May-25 4 In an experiment on photoelectric effect, a beam of light is used and the voltage across the electrodes required to stop the photocurrent is 1.5 V. (a) Determine the maximum speed of the photoelectrons. (b) Sketch a graph to illustrate how the photocurrent varies with the voltage across the electrodes and label it (b). (c) With reference to photoelectrons, explain the significance of the sloping section of your graph