Physics 102: Lecture 25, Slide 1 Periodic Table, Atomic Structure Today’s Lecture will cover Section 28.7 Physics 102: Lecture 25 Make sure your grade book entries are correct.

Quantum Numbers Each electron in an atom is labeled by 4 #’s n = Principal Quantum Number (1, 2, 3, …) Determines energy m s = Spin Quantum Number (+½, -½) “Up Spin” or “Down Spin” ℓ = Orbital Quantum Number (0, 1, 2, … n-1) Determines angular momentum m ℓ = Magnetic Quantum Number ( ℓ, … 0, … - ℓ ) Component of ℓ

Physics 102: Lecture 25, Slide 3 Preflight 25.1 For which state of hydrogen is the orbital angular momentum required to be zero? n=3 n=2 n=1

Physics 102: Lecture 25, Slide 4 Preflight 25.1 For which state of hydrogen is the orbital angular momentum required to be zero? n=3 n=2 n=1 The allowed values of ℓ are 0, 1, 2, …, n-1. When n=1, ℓ must be zero.

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: 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 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”

Physics 102: Lecture 25, Slide 7 Quantum Numbers How many unique electron states exist with n=2?

Physics 102: Lecture 25, Slide 8 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 9 ACT: Quantum Numbers How many unique electron states exist with n=5 and m l = +3?

Physics 102: Lecture 25, Slide 10 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 = +3

Physics 102: Lecture 25, Slide 11 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 12 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 13 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

Physics 102: Lecture 25, Slide 14 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 15 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 16 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

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.

Physics 102: Lecture 25, Slide 19 See you later! Read Textbook Section 27.4 ICES Forms – Don’t Leave Yet!