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Physics 21900 General Physics II Electricity, Magnetism and Optics Lecture 26 – Chapter 27 Photons, The Hydrogen Atom, de Broglie Waves Fall 2015 Semester Prof. Matthew Jones Review • Photons are quanta of electromagnetic radiation • Energy can be measured in electron-volts: = . × • The energy of a photon depends on its frequency: = = . × ∙ (Planck’s constant) = . × ∙ • Wavelength is related to frequency: = • Energy is related to wavelength: = Bohr’s model for light emission from H Size of the hydrogen atom = 0.53 × 10 m "# , for " = 1,2,3, … • " is called the principal quantum number and must be a positive integer • Only certain radii represent stable electron orbits. = "# ' ' = 0.0529nm Energy of Electron orbits • • • • 13.6, = − "# Negative energies mean the electron is bound to the nucleus. " = 1 is the lowest possible energy (the ground state). A free electron has > 0. A photon is absorbed or emitted when an " changes. ∆ = 0 − 1 Photon Emission and Photon Absorption Example • What is the wavelength of a photon emitted when an electron drops from the " = 3 orbit to the ground state? 13.6,0 = − = −1.51,# 3 13.6,1 = − = −13.6,# 1 ∆ = 0 − 1 = 12.1, 4.14 × 104 ,- ∙ 5 3 × 106 7⁄5 = = 12.1,Δ = 1.03 × 109 7 = 103"7 (extreme ultraviolet) Example What is the minimum energy needed to ionize a hydrogen atom that has its electron in the " = 2 orbit? • Bound electrons have < 0 • The minimum energy of a free electron is = 0 13.6,0 = − = −3.4,# 2 1 = 0 (minimum possible) Minimum photon energy is = 3.4,• Wavelength, = ;< = = >.>× ?@A BC∙D E× F G⁄D E.>BC = 365"7 (ultraviolet) Example What is the de Broglie wavelength of an electron that is accelerated from rest through a potential difference of 100 V? 1. Kinetic energy is 1 H = 7B I # = 100,- = 1.602 × 109 J 2 2. Momentum is K = 7B I = 27B H = 2(9.109 × 10E MN)(1.602 × 109 J) = 5.40 × 10#> MN ∙ 7/5 Example What is the de Broglie wavelength of an electron that is accelerated from rest through a potential difference of 100 V? 3. de Broglie wavelength is = K 6.626 × 10E> J ∙ 5 = = 0.123"7 #> 5.40 × 10 MN ∙ 7/5 If electrons behave like waves, can we observe interference phenomena? A double slit experiment will need a slit spacing that is less than 1 nm! Atomic Quantum Numbers Principal quantum number, ". Mainly determines the energies of bound electrons. Atomic Quantum Numbers • Sommerfeld extended the Bohr model to account for quantized angular momentum • A new quantum number, ℓ, known as the orbital quantum number, identifies the orbital angular momentum of a state. 0≤ℓ≤"−1 Atomic Quantum Numbers • A third quantum number, the magnetic quantum number, 7ℓ , is related to the orientation of the angular momentum vector ST = 7ℓ 2U ℓ Atomic Quantum Numbers • Electrons have an intrinsic angular momentum called “spin” which can have two possible values: 1 7D = ± 2 • Although electrons are point-like particles, they behave like little bar magnets. • This property has no analogous concept in classical mechanics. Summary of Quantum Numbers • Principal quantum number: • Orbital angular momentum quantum number: • Magnetic quantum number: • Spin magnetic quantum number: Pauli’s Exclusion Principle • No two electrons can have the same set of quantum numbers. • Each electron has a unique set of ", ℓ, 7ℓ , 7D • Example: The number of states and the quantum number designation of each state for the ℓ = 2 subshell: Atomic subshells from lowest to highest energy (approximate) 2 in the top row 8 in the second row 8 in the third row 18 in the fourth row … Atomic Electron Configurations Heisenberg Uncertainty Principle