Announcements. Chapter. 8 Spin & Atomic Physics SPIN. For and electron: s = 1/2. s the quantum number of SPIN. Intrinsic property of a particle

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1 Announcements! HW8 : Chap.8 30, 31, 35, 41, 49! Physics Colloquium: Development in Electron Nuclear Dynamics Theory on 3:40pm! Quiz3: 4/19 (Chap. 6,7,8) *** Course Web Page ** Lecture Notes, HW Assignments, Schedule for thephysics Colloquium, etc.. Outline: Chapter. 8 Spin & Atomic Physics! Evidence of Angular Momentum Quantization! Identical Particles! The Exclusion Principle! Multi-electron Atoms & the Periodic Table! Characteristic X-Rays It s open said that in Q.M. there re only 3 bound-state problems solvable (w/o numerical approximation tech.) 1.! Infinite well, 2. Harmonic oscillation, 3. hydrogen atom all 1-particle problem. Most real application: multiple system. so, start an atom with multiple electrons SPIN A given particle s intrinsic magnetic dipole moment is related to intrinsic angular m/m, S gyromagnetic ratio For and electron: s = 1/2 Intrinsic angular momentum: Like for L: s the quantum number of SPIN e.g. for proton s = 1/2, for W, s = 1, see Table 8.1 (p295) Intrinsic property of a particle

2 Spin Orientation 2 possible spin states of an electron Stern-Gerlach Experiment? spin quantum number: allowed values are from s to +s in integral steps Now let us return to the Stern-Gerlach experiment. For l =0, the orbital magnetic moment µ L = 0, so it shouldn t be subject to a force, but there should still be a force on the intrinsic magnetic dipole moment. Sz 1 = ±! 2 for electrons spin quantum #: +- 1/2 The Stern-Gerlach Experiment 2 lines corresponding to m s = -1/2 & +1/2 S z 1 = ± 2! F = ±F 0 Schrodinger Equation for two Electrons SPIN = 1/2

3 Schrodinger Equation for two Electrons Schrodinger Equation for two Electrons Simple: 2 Particles in a Box a: x 1 b: x 2? 2 particles in the same box 2 particles in the same box

4 2 particles in the same box Inserting C1 & C2 into (8-16) yield E 2 particles in the same box: Example: n = 4, n = 3 The system s multi-particle wave function: The total E of the two particle system is the sum of the individual infinite well energies in state n&n Total Probability density: 2 particles in the same box: Total Probability density: P(x1,x2) as a function of 2 variables x1, x2 Example: n = 4, n = 3 Inserting x 1 = (1/2)L Example: n = 4, n = 3 Prob. of finding particle 2 at the center (i.e. x 2 = (1/2)L) is non-zero 4 bumps 3 bumps This Should NOT happen because particles 1 and 2 are indistinguishable Identical particles sharing the same space are said to be

5 Symmetric Solutions Solution: Symmetry The largest values of P S occur where the particles are close together (near x 1 = x 2 ) P A has its largest bumps when x 1 ~ L & x 1 ~ 0 x 2 ~ 0 & x 2 ~ L x 1 = x 2! 0 All Elementary Particles: either Bosons or Fermions Q: Why is spin so crucial to the behavior of multi-particle system? Bosons particle for which s = 0,1,2, Fermions particle for which s =1/2, 3/2, 5/2,

6 Some Bosons and Fermions The Pauli Exclusion Principle for Fermions 1 1 S z = +! S z = +! 2 2 The Exclusion Principle for Fermions The Exclusion Principle for Fermions 1 1 S z = +! S z =!! S z = +! S =!! 2 z 2 O.K. S z 1 = +! 2

7 The Exclusion Principle for Fermions Let s create multi-electron atoms Our Toolkit: 1 1 S z = +! S =!! 2 z 2 S z 1 = +! 2 May never happen The Schrodinger Equation Quantization of Energy Levels The Exclusion Principle Progressive Occupation of Energy Levels Hydrogen H Helium He

8 Energy Levels Lithium Li (3 electrons) Hydrogen H, ground state Energy Levels Energy Levels He 2-electrons Neon (Ne) 10-electrons

9 Energy Levels Neon Ne 1s 2 2s 2 2p = 10 Fluorine: 9-electrons 1s 2 2s 2 2p 5 Fluorine F Like Ne with one electron (and proton) less 1s 2 2s 2 2p = 9 Fluorine F Like Ne with one electron (and proton) less A fluorine atom would gladly accept one more electron, to look more like Ne That s why it is chemically very reactive

10 What matters for Chemical Properties is the state of the most loose electrons What maters for Chemical Properties is the state of the most loose electrons The other, more strongly bound electrons are merely passive placeholders The traditional naming scheme Principal quantum number n The number of electrons in that subshell

11 Noble gasses Noble gasses He + 1 electron Li: 1s 2 2s 1 First Ionization Energy VALENCE

12 Alkali metals