RI Chap 19 Quantum Physics Lecture Notes

19 Quantum Physics H2 Physics 9478 Content Page Introduction 2 19.1 The Photoelectric Effect 3 19.2 Wave-Particle Duality 5 19.3 Wavefunction of a Particle 8 19.4 Energy Levels of Atoms and Line Spectra 18 19.5 Heisenberg Uncertainty Principle 27 19.6 Appendix 29 Learning Outcomes Candidates should be able to: (a) show an understanding that the existence of a threshold frequency in the photoelectric effect provides evidence that supports the particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence that supports its wave nature (b) state that a photon is a quantum of electromagnetic radiation, and recall and use the equation E hf= for the energy of a photon to solve problems, where h is the Planck constant (c) show an understanding that while a photon is massless, it has a momentum given by p Ec= and ph λ= , where c is the speed of light in free space (d) show an understanding that electron diffraction and double- slit interference of single particles provide evidence that supports the wave nature of particles (e) recall and use the equation hpλ = for the de Broglie wavelength to solve problems (f) show an understanding that the state of a particle can be represented as a wavefunction ψ, e.g. for an electron cloud in an atom, and that the square of the wavefunction amplitude 2 ψ is the probability density function (including calculation of normalisation factors for square and sinusoidal wavefunctions) (g) show an understanding that the principle of superposition applies to the wavefunctions describing a particle’s position, leading to standing wave solutions for a particle in a box and phenomena such as single-particle interference in double-slit experiments (h) show an understanding that the Heisenberg position- momentum uncertainty principle xp h∆∆ >  relates to the necessity of a spread of momenta for localised particles, and apply this to solve problems (i) show an understanding of standing wave solutions 𝜓𝜓 n for the wavefunction of a particle in a one- dimensional infinite square well potential

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 2 (j) solve problems using 2 2 28 n hEn mL= for the allowed energy levels of a particle of mass m in a one- dimensional infinite square well of width L (k) show an understanding of the existence of discrete electronic energy levels for the electron’s wavefunction 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) solve problems involving photon absorption or emission during atomic energy level transitions. Introduction Wave theory of light has been highly successful in describing phenomena such as diffraction, interference and polarisation, leading to the creation of radio waves, radar and optical filters, just to name a few. However, w