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Physics 102: Lecture 25 Atomic Spectroscopy & Quantum Atoms Physics 102: Lecture 25, Slide 1 PICK UP A DIFFRACTION GRATING! From last lecture – Bohr model Angular momentum is quantized Ln = nh/2π n = 1, 2, 3 ... Energy is quantized mk 2e4 Z 2 13.6 Z 2 En eV where h / 2 2 2 2 2 n n Radius is quantized 2 2 n2 h 1 n rn 0.0529 nm 2 Z 2 mke Z Velocity too! Physics 102: Lecture 25, Slide 2 +Ze Transitions + Energy Conservation • Each orbit has a specific energy: En= -13.6 Z2/n2 • Photon emitted when electron jumps from high energy to low energy orbit. Photon absorbed when electron jumps from low energy to high energy: E2 – E1 = h f = h c / l Physics 102: Lecture 25, Slide 3 E2 E1 Demo: Line Spectra In addition to the continuous blackbody spectrum, elements emit a discrete set of wavelengths which show up as lines in a diffraction grating. 656 nm H n=3 n=2 This is how neon signs & Na lamps work! Spectra give us information on atomic structure Physics 102: Lecture 25, Slide 4 n=1 Solar spectrum! Physics 102: Lecture 25, Slide 5 Checkpoint 1.1 Electron A falls from energy level n=2 to energy level n=1 (ground state), causing a photon to be emitted. Electron B falls from energy level n=3 to energy level n=1 (ground state), causing a photon to be emitted. n=3 n=2 Which photon has more energy? 1) Photon A 2) Photon B A B n=1 Physics 102: Lecture 25, Slide 6 Spectral Line Wavelengths Calculate the wavelength of photon emitted when an electron in the hydrogen atom drops from the n=2 state to the ground state (n=1). E2= -3.4 eV n=3 n=2 Z2 E n 13.6eV 2 n hf E2 E1 3.4eV (13.6eV) 10.2eV E1= -13.6 eV Ephoton Physics 102: Lecture 25, Slide 7 n=1 hc l hc 1240 l 124nm 10.2eV 10.2 ACT: Spectral Line Wavelengths Compare the wavelength of a photon produced from a transition from n=3 to n=2 with that of a photon produced from a transition n=2 to n=1. A l32 < l21 B l32 = l21 C l32 > l21 E32 < E21 Physics 102: Lecture 25, Slide 8 so n=3 n=2 l32 > l21 n=1 ACT/Checkpoint 1.2 The electrons in a large group of hydrogen atoms are excited to the n=3 level. How many spectral lines will be produced? A. 1 B. 2 n=3 n=2 C. 3 D. 4 E. 5 n=1 Physics 102: Lecture 25, Slide 9 The Bohr Model is incorrect! To be consistent with the Heisenberg Uncertainty Principle, which of these properties cannot be quantized (have the exact value known)? (A=OK B= NOT ) Electron Radius Would know location Electron Energy Electron Velocity Would know momentum Electron Angular Momentum But, in the Bohr model: 2 2 2 h 1 n n rn 0.0529 nm 2 Z 2 mke Z Physics 102: Lecture 25, Slide 10 Quantized radii and velocities for electron orbitals Checkpoint 2 +Ze Bohr Model Quantum Atom So what keeps the electron from “sticking” to the nucleus? 21% 36% 42% A) Centripetal Acceleration B) Pauli Exclusion Principle C) Heisenberg Uncertainty Principle Physics 102: Lecture 25, Slide 11 Quantum Mechanics Theory used to predict probability distributions QM Physics 102: Lecture 25, Slide 12 Quantum Mechanical Atom • Predicts available energy states agreeing with Bohr. • Don’t have definite electron position, only a probability function. • Each orbital can have 0 angular momentum! • Each electron state labeled by 4 numbers: n = principal quantum number (1, 2, 3, …) l = angular momentum (0, 1, 2, … n-1) ml = component of l (-l < ml < l) ms = spin (-½ , +½) Physics 102: Lecture 25, Slide 13 Quantum Mechanics (vs. Bohr) Electrons are described by a probability function, not a definite radius! It takes 4 numbers to describe the electron Bohr: just 𝑛 Each orbital 𝑛 can have 0 angular momentum Bohr: 𝐿𝑛 = 𝑛 ℏ n = 1,2,3 … Physics 102: Lecture 25, Slide 14 Quantum Numbers Each electron in an atom is labeled by 4 #’s n = Principal Quantum Number (1, 2, 3, …) • Determines the Bohr energy l = Orbital Quantum Number (0, 1, 2, … n-1) • • Determines angular momentum l <n always true! L h ( 1) 2 ml = Magnetic Quantum Number (-l , … 0, … l ) • • z-component of l | ml | <= l always true! ms = Spin Quantum Number (-½ , +½) • “Up Spin” or “Down Spin” Physics 102: Lecture 25, Slide 15 h Lz m 2 ACT: Quantum numbers For which state of hydrogen is the orbital angular momentum required to be zero? 1. n=1 2. n=2 3. n=3 Physics 102: Lecture 25, Slide 16 The allowed values of l are 0, 1, 2, …, n-1. When n=1, l must be zero. Spectroscopic Nomenclature “Shells” “Subshells” l =0 is “s state” l =1 is “p state” l =2 is “d state” l =3 is “f state” l =4 is “g state” n=1 is “K shell” n=2 is “L shell” n=3 is “M shell” n=4 is “N shell” n=5 is “O shell” 1 electron in ground state of Hydrogen: n=1, l =0 is denoted as: 1s1 n=1 Physics 102: Lecture 25, Slide 17 l =0 1 electron Quantum Numbers How many unique electron states exist with n=2? l = 0 : 2s2 ml = 0 : ms = ½ , -½ 2 states l = 1 : 2p6 ml = +1: ms = ½ , -½ ml = 0: ms = ½ , -½ ml = -1: ms = ½ , -½ 2 states 2 states 2 states There are a total of 8 states with n=2 Physics 102: Lecture 25, Slide 18 Electron orbitals In correct quantum mechanical description of atoms, positions of electrons not quantized, orbitals represent probabilities Carbon orbitals imaged in 2009 using electron microscopy! Physics 102: Lecture 25, Slide 19 ACT: Quantum Numbers How many unique electron states exist with n=5 and ml = +3? A) 0 B) 4 C) 8 D) 16 E) 50 l l l l = 0 : ml = 0 = 1 : ml = -1, 0, +1 = 2 : ml = -2, -1, 0, +1, +2 Only l = 3 and l = 4 have ml = +3 = 3 : ml = -3, -2, -1, 0, +1, +2, +3 ms = ½ , -½ 2 states l = 4 : ml = -4, -3, -2, -1, 0, +1, +2, +3, +4 ms = ½ , -½ 2 states There are a total of 4 states with n=5, ml = +3 Physics 102: Lecture 25, Slide 20 Pauli Exclusion Principle In an atom with many electrons only one electron is allowed in each quantum state (n, l, ml, ms). This explains the periodic table! Physics 102: Lecture 25, Slide 21 Electron Configurations # electrons Atom Configuration 1 2 H He 1s1 1s2 3 Li 1s22s1 4 Be 1s22s2 5 B etc 1s22s22p1 10 Ne (n=1 shell filled noble gas) 2s shell filled 1s22s22p6 s shells hold up to 2 electrons Physics 102: Lecture 25, Slide 22 1s shell filled 2p shell filled (n=2 shell filled noble gas) p shells hold up to 6 electrons The Periodic Table s (l =0) n = 1, 2, 3, ... p (l =1) Also s d (l =2) f (l =3) What determines the sequence? Pauli exclusion & energies Physics 102: Lecture 25, Slide 23 Summary • Each electron state labeled by 4 numbers: n = principal quantum number (1, 2, 3, …) l = angular momentum (0, 1, 2, … n-1) ml = component of l (-l < ml < l) ms = spin (-½ , +½) • Pauli Exclusion Principle explains periodic table • Shells fill in order of lowest energy. Physics 102: Lecture 25, Slide 24