Physics 102: Lecture 25, Slide 1 Periodic Table, Atomic Structure Physics 102: Lecture 25

Physics 102: Lecture 25, Slide 2 From last lecture – Bohr model L n = nh/2π Angular momentum is quantized Energy is quantized Radius is quantized n = 1, 2, 3... Linear momentum too Bohr model is incorrect!

Physics 102: Lecture 25, Slide 3 Quantum Numbers Each electron in an atom is labeled by 4 #’s n = Principal Quantum Number (1, 2, 3, …) Determines energy (Bohr) m s = Spin Quantum Number (-½, +½) “Up Spin” or “Down Spin” l = Orbital Quantum Number (0, 1, 2, … n-1) Determines angular momentum l < n always true! m l = Magnetic Quantum Number (- l, … 0, … l ) Component of l | m l | <= l always true! Note differences with Bohr model

Physics 102: Lecture 25, Slide 4 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 5 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” 1 electron in ground state of Hydrogen: n=1, l =0 is denoted as: 1s 1 n=1 l =0 1 electron Spectroscopic Nomenclature “Subshells”“Shells” 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”

Physics 102: Lecture 25, Slide 6 Electron orbitals In correct quantum mechanical description of atoms, positions of electrons not quantized, orbitals represent probabilities

Physics 102: Lecture 25, Slide 7 Quantum Numbers How many unique electron states exist with n=2? l = 0 : m l = 0: m s = ½, -½ 2 states l = 1 : m l = +1: m s = ½, -½ 2 states m l = 0: m s = ½, -½ 2 states m l = -1: m s = ½, -½ 2 states 2s 2 2p 6 There are a total of 8 states with n=2

Physics 102: Lecture 25, Slide 8 ACT: Quantum Numbers How many unique electron states exist with n=5 and m l = +3? A) 0 B) 4 C) 8 D) 16 E) 50

Physics 102: Lecture 25, Slide 9 Preflight 25.2 What is the maximum number of electrons that can exist in the 5g (n=5, l =4) subshell of an atom?

Physics 102: Lecture 25, Slide 10 In an atom with many electrons only one electron is allowed in each quantum state (n, l, m l, m s ). Pauli Exclusion Principle This explains the periodic table!periodic table!

Physics 102: Lecture 25, Slide 11 Atom Configuration H1s 1 He1s 2 Li1s 2 2s 1 Be1s 2 2s 2 B1s 2 2s 2 2p 1 Ne1s 2 2s 2 2p 6 1s shell filled 2s shell filled 2p shell filled etc (n=1 shell filled - noble gas) (n=2 shell filled - noble gas) Electron Configurations p shells hold up to 6 electronss shells hold up to 2 electrons

Physics 102: Lecture 25, Slide 12 s ( l =0) p ( l =1) d ( l =2) f ( l =3) n = 1, 2, 3,... The Periodic Table What determines the sequence?Pauli exclusion & energies Also s

Physics 102: Lecture 25, Slide 13 2s electrons can get closer to nucleus, which means less “shielding” from the 1s electrons Shell Ordering Why do s shells fill first before p? r 2p P(r) r 2s P(r) 1s

Physics 102: Lecture 25, Slide 14 Sequence of shells: 4s electrons get closer to nucleus than 3d Sequence of Shells 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d... 1s,2s,2p,3s,3p,4s,3d,4p, Pneumonic:...

Physics 102: Lecture 25, Slide 15 Properties of elements We can understand the different properties of elements from the periodic table Noble gases Filled outer p-shell (s for He) Hard to ionize Non-reactive Alkali metals Unpaired outer s-shell e – Easy to ionize Very reactive Transition metals Filling d-shell ( l = 2) Tend to be magnetic s2p6s2p6 s1s1 d 1 – d 10

Physics 102: Lecture 25, Slide 16 Transition elements Recall torque on current loop from B-field:  = IABsin(  ) IA = -ep/(2  rm) (  r 2 ) = -(e/2m)rp = -(e/2m)L T = 2  r/v = 2  r/v = 2  rm/p In 3d shell we are putting electrons into l = 2; all atoms in middle are strongly magnetic. Why? High angular momentum Strongly magnetic! Use Bohr model: Ze e–e– This looks like a current loop! I I = -e/T A =  r 2 r Angular momentum!

Physics 102: Lecture 25, Slide 17 Yellow line of Na flame test is 3p 3s Na 1s 2 2s 2 2p 6 3s 1 Neon - like core Many spectral lines of Na are outer electron making transitions Single outer electron Sodium

Physics 102: Lecture 25, Slide 18 Summary Each electron state labeled by 4 numbers: n = principal quantum number (1, 2, 3, …) l = angular momentum (0, 1, 2, … n-1) m l = component of l (- l < m l < l ) m s = spin (-½, +½) Pauli Exclusion Principle explains periodic table Shells fill in order of lowest energy.