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Periodic Table, Atomic Structure

Physics 102: Lecture 25. Periodic Table, Atomic Structure. Today’s Lecture will cover Section 28.7. Make sure your grade book entries are correct. n = Principal Quantum Number (1, 2, 3, …). Determines energy. ℓ = Orbital Quantum Number (0, 1, 2, … n-1).

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Periodic Table, Atomic Structure

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

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

  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 3

  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 4

  5. 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: Physics 102: Lecture 25, Slide 5

  6. 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 Physics 102: Lecture 25, Slide 6

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

  8. 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 Physics 102: Lecture 25, Slide 8

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

  10. ACT: Quantum Numbers How many unique electron states exist with n=5 and mℓ = +3? 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 Physics 102: Lecture 25, Slide 10

  11. 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! Physics 102: Lecture 25, Slide 11

  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 12

  13. 18 states 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 mℓ= +3: ms = ½ , -½ 2 states mℓ = +4: ms = ½ , -½ 2 states Physics 102: Lecture 25, Slide 13

  14. 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 Physics 102: Lecture 25, Slide 14

  15. 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 Physics 102: Lecture 25, Slide 15

  16. 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 Physics 102: Lecture 25, Slide 16

  17. 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 Physics 102: Lecture 25, Slide 17

  18. 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. Physics 102: Lecture 25, Slide 18

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

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