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Transcript
PH 103 Dr. Cecilia Vogel Lecture 20 Review uncertainty atoms and nuclei The quantum model of the atom Outline Quantum numbers H-atom spectra Current Model of Atom Electron “cloud” is wavefunction describes the probability of electron being at various points around the nucleus. Electron wave behavior based on Schroedinger equation. The electron states are quantized 4 different quantities are quantized 4 different quantum numbers n, ℓ, mℓ, ms. http://www.falstad.com/qmatom/directions.html Four Quantum Numbers Quantum number n ℓ mℓ ms Physical quantity Possible values Positive Energy Size of orbital integers Orbital angular Non-negative momentum integers (Energy) Orb. ang. mom. integers z-component Spin z-component + ½ or - ½ Additional restrictions n>ℓ ℓ<n ℓ > |mℓ| |mℓ| < ℓ none Principle Quantum Number Principle quantum number, n, n = 1, 2, 3, 4, 5, .... Determines what “shell” the electron is in. n=1 is called the K-shell, n=2 is the L-shell, etc tells a lot about the electron’s energy for hydrogen atom, it determines the electron’s energy 13 . 6 eV for hydrogen atom: E n n 2 Hydrogen Ground State Consider the electron in hydrogen the ground state is the lowest energy state lowest E, lowest n, n = 1 Since n =1, then = 0 Since = 0, then m = 0 ms = ½ (2 possibilities) Ground state has a degeneracy of two because there are two states with the same E Transition Up Electron absorbs energy perhaps from a photon goes to a higher energy level ee photon Transition Up Some ways to add energy to the atom i.e. ways to excite electron: HEAT like blackbody radiation ZAP electric discharge through a gas SLAM hit atom with high-energy particle for example, nuclear radiation SHINE hit atom with light (photons) Transition Down – H-atom Electron loses energy to a photon - gives off light Electron goes to a lower energy level 13.6eV 13.6eV losing energy | E | nf 2 ni 2 ee- photon Transition Down – H-atom Electron loses energy to a photon - gives off light Light created has the energy that the electron lost so 13.6eV 13.6eV Ephoton 2 2 nf ni hc 13.6eV 13.6eV 2 2 nf ni Hydrogen spectrum Visible lines in H-spectrum come from transitions to nf=2. Ex: with ni=3 hc 13.6eV 13.6eV 2 nf ni 2 1240eVnm 13.6eV 13.6eV 4 9 656 nm H and Multi-electron Atoms Recall for Hydrogen electron Energy depends on n only Other atoms electron energy depends on n and ℓ So… L-shell (n=2) for hydrogen atom is just one energy level L-shell for other atoms -- two different energy levels 2s and 2p and M-shell splits into 3s, 3p, 3d subshells, etc Single-electron atoms (like Hydrogen) Other atoms Compare Hydrogen to Multi-electron Atoms Hydrogen has few e- energy levels few e- transitions few photon energies, few wavelengths Other atoms many e- energy levels many e- transitions many photon energies, many wavelengths generally have more complicated spectrum