Periodic Table, Atomic Structure Physics 102: Lecture 25 Make sure your grade book entries are correct. Hour Exam III average = 76.8%. Nice work!

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! 10

ACT For which state of hydrogen is the orbital angular momentum required to be zero? 1. n=1 2. n=2 3. n=3 The allowed values of l are 0, 1, 2, …, n-1. When n=1, l must be zero % 15% 10%

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 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” 14

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 16

ACT: Quantum Numbers How many unique electron states exist with n=5 and m l = +3? l = 0 : m l = 0 l = 1 : m l = -1, 0, +1 There are a total of 4 states with n=5, m l = +3 l = 2 : m l = -2, -1, 0, +1, +2 l = 3 : m l = -3, -2, -1, 0, +1, +2, +3 m s = ½, -½ 2 states l = 4 : m l = -4, -3, -2, -1, 0, +1, +2, +3, +4 m s = ½, -½ 2 states Only l = 3 and l = 4 have m l = A) 0 B) 4 C) 8 D) 16 E) 50

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! 25

Preflight 25.2 What is the maximum number of electrons that can exist in the 5g (n=5, l =4) subshell of an atom? m l = -4 : m s = ½, -½ 2 states m l = -3 : m s = ½, -½2 states m l = -2 : m s = ½, -½ 2 states 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 m l = +2: m s = ½, -½ 2 states m l = +3: m s = ½, -½ 2 states m l = +4: m s = ½, -½ 2 states 18 states 2*9 27 in general, 2*(2l+1)

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 29

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 31

Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p….. 4s electrons get closer to nucleus than 3d Sequence of Shells 33 1s 2p 3p 4p 5p 4f 5f

Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p….. 4s electrons get closer to nucleus than 3d 24 Cr 26 Fe 19 K 20 Ca 22 Ti 21 Sc 23 V 25 Mn 27 Co 28 Ni 29 Cu 30 Zn 4s 3d 4p In 3d shell we are putting electrons into l = 2; all atoms in middle are strongly magnetic. Angular momentum Loop of current Large magnetic moment Sequence of Shells 33

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 35

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. 40