ASRJC Quantum Physics

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 19-1 Additional Notes Topic 19: Quantum Physics Content: A The energy of a photon and the photoelectric effect B Wave-particle duality C Energy levels in atoms D Line spectra E X-ray spectra F The uncertainty principle Learning Outcomes: Candidates should be able to: (a) show an appreciation of the particulate nature of electromagnetic radiation (b) recall and use E = hf for the energy of a photon (c) show an understanding that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence for the wave nature (d) recall the significance of threshold frequency (e) recall and use the equation ½ mvmax2 = eVs, where Vs is the stopping potential. (f) explain photoelectric phenomena in terms of photon energy and w ork function energy (g) explain why the stopping potential is independent of intensity whereas the photoelectric current is proportional to intensity at constant frequency (h) recall, use and explain the significance of the equation hf =  + ½mvmax2 (i) describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles (j) recall and use the relation for the de Broglie wavelength λ=  h (k) show an understanding of the existence of discrete electron energy levels in isolated atoms (e.g. atomic hydrogen) and deduce how this leads to the observation of spectral lines (l) distinguish between emission and absorption line spectra. (m) recall and solve problems by using the relation hf = E2 - E1 (n) explain the origins of the features of a typical X-ray spectrum (o) show an understanding of and apply ∆ρ∆x ≳ h as a form for the Heisenberg position-momentum uncertainty principle to new situations or to solve related problems. Lecture SOW Lect Concepts Questions Est. Video Time 1 A.1 – A.4 CYU1 38 min 2 A.5 – A.8 CYU2, CYU3 and Example 1 41 min 3 B.1, B.2 and C Example 2, Example 3, Example 4, CYU 4 40 min 4 C.1 - D.3 CYU5 and CYU6 37 min 5 E.1 – E.3 Example 5, Example 6 37 min 6 F Example 7, Example 8 and Example 9 14 min

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 19-2 Additional Notes • In earlier topics we learnt that phenomena such as interference and diffraction are exhibited by light as it is passed through slits in Young’s double slits experiment. • These observations provide evidence for a wave nature of electromagnetic radiation. • However, when we look at observations associated with the photoelectric effect, we discover a completely different aspect of light. • We find that the energy of electromagnetic radiation is quantized; it is emitted and absorbed in particle-like packages of definite energy. A.1 The Experimental Setup A The Photoelectric Effect Photoelectric effect is the ejection of an electron from a metal surface when the surface is irradiated with electromagnetic radiation of a high enough frequency. _ _ _ _ _ _ _ _ electrons free electrons within metal clean metallic surface (e1) (e3) (e2) lamp E.M. radiation V A emitter collector incident radiation - - - - Gold leaf oscilloscope showing photoelectric effect Video on Photoelectric Experiment:

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 19-3 Additional Notes • The components include: ➢ emitter and collector plates ➢ vacuum tube (to ensure that emitted photoelectrons are not obstructed by air molecules) ➢ variable emf (to produce a potential difference between emitter and collector) ➢ voltmeter measures the potential difference V between emitter and collector, taken with respect to the emitter ➢ ammeter measures the magnitude of the photocurrent (i) The photoelectric effect The emitter plate (a metal plate) is irradiated with electromagnetic radiation, and electrons are emitted from the emitter plate. These photoelectrons leave the plate with a range of kinetic energies – some move faster than the others. The stream of photoelectrons which manage to reach the collector plate complete the circuit and constitute a photocurrent (i). A.2 Measuring the maximum KE of photoelectrons When radiation of sufficiently high frequency is irradiated on the emitter, by varying the potential difference V across the collector and emitter, the photocurrent i detected may change, as shown in the graph below. i V imax 0 -Vs (3) (2) (1) (4) (5) Photoelectrons are electrons emitted via the photoelectric effect.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 19-4 Additional Notes The following scenarios explain the various parts labelled in the graph. Scenario Explanation 1 Collector is at the same potential as emitter (V = 0). No electric field is exists between the plates. Electrons emitted in random directions. Only photoelectrons travelling towards the collector reached it (i.e. not all electrons reached collector) Rate of electrons leaving emitter > rate of electrons arriving at collector 2 Collector is at a slightly higher potential than emitter. More electrons reach the collector (i.e. electrons that may have been directed away from collector is now attracted towards it), although the electric field is not strong enough to draw all of them towards the collector. As compared to Scenario 1, now the rate of electrons arriving at collector increases, thus photocurrent increases. 3 Collector is at much higher potential than emitter. Electric field between plates is strong enough such that all photoelectrons reach the collector. Rate of electrons leaving emitter = rate of electrons arriving at collector Any further increase in potential difference between the plates does not lead to increase in photocurrent. Photocurrent is maximum (saturation current). - - emitter collector - - - - - - emitter collector - - - - emitter collector - - - - - - Saturation Current: Even though potential difference increases and there is a greater force on each electron and they accelerate more, the total number of electrons emitted per second did not increase. E.g. in 1 second, 10 electrons are emitted. The current is determined by I = dQ/dt, which is the total charge reaching collector plate per unit time. Even if these 10 electrons move with higher speed between emitter and collector, total charge reaching per second remains the same. Drift velocity cannot be applied directly as the space between collector and emitter is a vacuum.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 19-5 Additional Notes 4 The polarity of the e.m.f. source is reversed. Collector is at a lower potential than emitter. Electric field causes photoelectrons with lower KE to be repelled from collector. Only those with greater KE reach the collector. Hence, less electrons reach the collector. As compared to Scenario 1, now the rate of electrons arriving at collector decreases, thus photocurrent decreases. 5 From Scenario 4, any increase in the potential difference (V became more negative) lead to decrease in photocurrent. At the value of V when photocurrent just reached zero, the electric field is strong enough such that even photoelectrons with the greatest KE do not have sufficient energy to reach the collector. They are just turned back. This potential difference is known as the stopping potential (Vs). When this happens, a photoelectron with KEmax would have used up all its energy to do work against the electric field, i.e. The stopping potential Vs is