Periodic Table, Atomic Structure

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

2. From last lecture – Bohr model Angular momentum is quantized Ln= nh/2π n = 1, 2, 3 ... Energy is quantized Radius is quantized Momentum too

3. n = Principal Quantum Number (1, 2, 3, …) • Determines energy (Bohr) l = Orbital Quantum Number (0, 1, 2, … n-1) • Determines angular momentum • l < n always true! ml = Magnetic Quantum Number (-l , … 0, … l ) • Component of l • | ml | <= l always true! ms = Spin Quantum Number (-½ , +½) • “Up Spin” or “Down Spin” Quantum Numbers Each electron in an atom is labeled by 4 #’s 10

4. ACT For which state of hydrogen is the orbital angular momentum required to be zero? 75% 15% 10% 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

5. n=1 l =0 1 electron Nomenclature “Shells” “Subshells” l=0 is “s state” n=1 is “K shell” l=1 is “p state” n=2 is “L shell” l=2 is “d state” n=3 is “M shell” l=3 is “f state” n=4 is “N shell” l=4 is “g state” n=5 is “O shell” Example 1 electron in ground state of Hydrogen: n=1, l=0 is denoted as:1s1 14

7. Example Quantum Numbers How many unique electron states exist with n=2? l = 0 : ml = 0 : ms = ½ , -½ 2 states 2s2 l = 1 : ml = +1: ms = ½ , -½ 2 states ml = 0: ms = ½ , -½ 2 states ml = -1: ms = ½ , -½ 2 states 2p6 There are a total of8 stateswith n=2 16

8. 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 Only l = 3 and l = 4 have ml = +3 l = 0 : ml = 0 l = 1 : ml = -1, 0, +1 l = 2 : ml = -2, -1, 0, +1, +2 l = 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 of4 stateswith n=5, ml = +3 20

9. 18 states 2*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? ml = -4 : ms = ½ , -½ 2 states ml = -3 : ms = ½ , -½2 states ml = -2 : ms = ½ , -½ 2 states ml = -1 : ms = ½ , -½ 2 states ml = 0 : ms = ½ , -½ 2 states ml = +1: ms = ½ , -½ 2 states ml = +2: ms = ½ , -½ 2 states in general, 2*(2l+1) ml = +3: ms = ½ , -½ 2 states ml = +4: ms = ½ , -½ 2 states 27

10. 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! 25

11. s shells hold up to 2 electrons p shells hold up to 6 electrons Electron Configurations Atom Configuration H 1s1 He 1s2 1s shell filled (n=1 shell filled - noble gas) Li 1s22s1 Be 1s22s2 2s shell filled B 1s22s22p1 etc (n=2 shell filled - noble gas) Ne 1s22s22p6 2p shell filled 29

13. 1s 1s P(r) 2s r 2s electrons can get closer to nucleus, which means less “shielding” from the 1s electrons Shell Ordering P(r) Why do s shells fill first before p? 2p r 31

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

15. 26 Fe 23 V 25 Mn 27 Co 28 Ni 29 Cu 30 Zn 20Ca 21Sc 22 Ti 24 Cr 19K 4s 4p 3d Sequence of Shells Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p….. 4s electrons get closer to nucleus than 3d 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 33

16. Single outer electron Neon - like core Yellow lineof Na flame test is 3p 3s Example Sodium Na 1s22s22p6 3s1 Many spectral lines of Na are outer electron making transitions www.WebElements.com 35

17. 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. 40