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Periodic Table, Atomic Structure

This lecture covers the quantum numbers associated with electrons in atoms, including the principal quantum number, orbital quantum number, magnetic quantum number, and spin quantum number. It explains how these quantum numbers determine the energy, angular momentum, and placement of electrons in shells and subshells. The lecture also discusses the Pauli Exclusion Principle and how it explains the filling order of electron shells in the periodic table.

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Periodic Table, Atomic Structure

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  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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

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