DHS 19 Quantum Physics (Notes & Tutorial)

Dunman High School (Senior High Physics Department) 9749 H2 Physics (2025) Topic 19: Quantum Physics 19-1 Content  Energy of a photon  The photoelectric effect  Wave-particle duality  Energy levels in atoms  Line spectra  X-ray spectra  The uncertainty principle Learning Outcomes Candidates should be able to: 9749 H2 Physics Topic 19 Quantum Physics Year 6 (2025) DUNMAN HIGH SCHOOL

Dunman High School (Senior High Physics Department) 9749 H2 Physics (2025) Topic 19: Quantum Physics 19-2 Guiding Questions  What roles do experiments play in constructing knowledge about the photoelectric effect, the discrete energy levels in atoms, and wave-particle duality?  How does the wave model of light fail to explain the photoelectric effect? What does the existence of atomic line spectra suggest about light?  How does quantum physics modify our ideas about matter?  How can we use conservation laws to analyse the photoelectric effect?  What is the significance of Heisenberg’s uncertainty principle? 19.0 Introduction Links between sections and topics Modern physics, developed from 1900 onwards, focuses on quantum and nuclear physics. It provides the foundation for much of chemistry and explains the behaviour of matter at the atomic scale, which differs significantly from classical Newtonian physics. Electromagnetic radiation exhibits both wave-like properties (interference, diffraction, polarisation) and particle-like behaviour (photoelectric effect, atomic spectra). This led to the concept of wave - particle duality, where electromagnetic radiation is composed of discrete 'photons' with energy proportional to frequency. Quantum physics introduced revolutionary ideas such as:  Quantisation of energy in atoms  Wave properties of particles (de Broglie wavelength)  Probabilistic nature of sub-atomic phenomena These concepts explained various experimental observations, including X -ray production and scattering, and led to technological advancements like lasers. While quantum mechanics challenged the deterministic view of the universe, it ultimately strengthened physics by providing a unified framework that encompasses both the microscopic and macroscopic realms. Applications and relevance to daily life Quantum mechanics plays a crucial role in our understanding of the world around us, particularly at the atomic and molecular level. It provides the foundation for explaining the structure of atoms and molecules, their emission and absorption spectra, chemical behaviours, and various material properties. This deep understanding has led to significant advancements in modern chemistry and materials science. Beyond its theoretical importance, quantum mechanics is paving the way for revolutionary technologies. One of the most exciting areas of development is quantum computing. Unlike traditional computers that use bits (0s and 1s), quantum computers utilise qub its, which can exist in a superposition of both states simultaneously, allowing quantum computers to process multiple possibilities at once. This field brings together experts from physics, computer science, and mathematics, promising to solve complex problems far more efficiently than classical computers.

Dunman High School (Senior High Physics Department) 9749 H2 Physics (2025) Topic 19: Quantum Physics 19-3 19.1 Photon Instead of treating electromagnetic radiation as a continuous wave, both Max Planck and Albert Einstein independently postulated electromagnetic radiation as discrete packets of energy which behave like particles. A photon is a discrete packet (or quantum) of energy of electromagnetic radiation. Energy of one photon is directly proportional to the frequency (f) of electromagnetic radiation, E = hf where h is the Planck constant (= 6.63 × 10–34 J s) Q1: Determine the energy in joule of a high-energy gamma photon of frequency 1026 Hz. E = hf = (6.63×10–34) (1026) = 6.63 × 10–8 J The example shows that the energy for a ‘high-energy’ photon is far less than 1.0 J. Hence the joule is not a convenient unit for measuring photon energies. The electronvolt (eV) is often used for such purposes. 1 eV is the energy gained by an electron when it is accelerated through a potential difference of 1 volt. Energy gain = QΔV = (1 e) (1 V) = (1.60 × 10–19 C) (1 V) = 1.60 ×10–19 J Therefore, 1 eV = 1.60 × 10–19 J. To convert from eV to J, multiply by 1.60 × 10–19 To convert from J to eV, divide by 1.60 × 10–19 Q2: Visible light has wavelength spanning from 400 nm (violet) to 700 nm (red). Find, in eV, the maximum energy of a photon of visible light. Emax = hfmax = hc/λmin = (6.63 × 10–34) (3.00 ×108) / (400 ×10–9) = 4.97 × 10–19 J = 3.11 eV

Dunman High School (Senior High Physics Department) 9749 H2 Physics (2025) Topic 19: Quantum Physics 19-4 Q3: Determine the number of photons emitted per second by a 60 W violet light source. Wavelength of the violet light source is 400 nm. Power of the light source = Total energy of light source per second = number of photons per second × energy of a violet photon 60 = n/t × 4.97 ×10–19 n/t = 1.21×1020 photons per second 19.2 Photoelectric effect The photoelectric effect refers to the emission of electrons (also known as photoelectrons) from a cold metal surface when electromagnetic radiation of a sufficiently high frequency falls on it. In 1905, Albert Einstein came up with an explanation for this phenomenon based on the idea of photons. metal surface e e e e photon E=hf A photon of energy hf is incident on the metal surface. metal surface e e e e photon E=hf Photon meets an electron. Electron absorbs the energy. metal surface e e e e Some energy is used to overcome the forces holding the electron in the metal, the rest is KE of the emitted electron. KE

Dunman High School (Senior High Physics Department) 9749 H2 Physics (2025) Topic 19: Quantum Physics 19-5 19.2.1 Einstein’s Photoelectric Equation energy provided by a single photon = work function energy of a metal + max KE of emitted electrons 21 max2hf mv  The work function energy Φ of a metal is the minimum energy of photon to cause emission of electron from surface of a metal. Work function energy depends on the nature of the material of the metal and its surface condition. The threshold frequency fo is the lowest frequency of electromagnetic radiation that gives rise to the ejection of electrons from the metal surface. The threshold wavelength λo is the highest wavelength of electromagnetic radiation that gives rise to the ejection of electrons from the metal surface.