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

2. 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

3. 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. 12 75% 15% 10%

4. 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

5. 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

6. 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 20 A) 0 B) 4 C) 8 D) 16 E) 50

7. 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

8. 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)

9. 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

11. 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

12. 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

13. 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

14. 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 www.WebElements.com 35

15. 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