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Atomic Physics and the Periodic Table

This lecture discusses the atomic structure and the periodic table, as well as the Pauli Exclusion Principle and the properties of different elements.

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Atomic Physics and the Periodic Table

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  1. Physics 3313 - Lecture 17 Wednesday March 31, 2010 Dr. Andrew Brandt • HW6 due today • Quiz on CH 7 today • Take Home quiz on CH6 handed out, due Monday 4/5/2010 (also can be printed from HW page of website) • HW7 assigned 4/1 due next Weds. 4/7 3313 Andrew Brandt

  2. CHAPTER 8Atomic Physics • 8.1 Atomic Structure and the Periodic Table • 8.2 Total Angular Momentum • 8.3 Anomalous Zeeman Effect What distinguished Mendeleev was not only genius, but a passion for the elements. They became his personal friends; he knew every quirk and detail of their behavior. - J. Bronowski 3313 Andrew Brandt

  3. Breaking News • http://podcasts.cnn.net/cnn/services/podcasting/newscast/CNN-News-09-17-06-3AM.mp3 • http://atlas.ch/ 3313 Andrew Brandt

  4. 8.1: Atomic Structure and the Periodic Table What would happen if there were more than one electron? a nucleus with charge +2e attracting two electrons. the two electrons repelling one another. Can not solve problems exactly with the Schrödinger equation because of the complex potential interactions. Can understand experimental results without computing the wave functions of many-electron atoms by applying the boundary conditions and selection rules. 3313 Andrew Brandt

  5. Pauli Exclusion Principle • Hydrogen atom electron is in ground state (lowest energy) • What about uranium? Are all 92 electrons in same quantum state? • 1925 Wolfgang Pauli says No! • No two electrons can have the same quantum numbers • He arrived at this by studying atomic spectra and looking at allowed transitions; unobserved lines correspond to states with two or more electrons having identical quantum numbers 3313 Andrew Brandt

  6. Consider Helium and Lithium 3313 Andrew Brandt

  7. Pauli Exclusion Principal • Consider a system of n non-interacting particles: • To simplify lets take n=2 identical particles with one particle in state a and another in state b • Probabilities should not depend on exchange of particles, since they are identical (probability of 1 in state a and 2 in state b should be equal to the probability of 2 in state a and 1 in b) • This implies the wave function can be either symmetric or anti-symmetric • Two possible combinations and • We don’t know which wave function defines system since particles are identical and equally probable, so must use a linear combination of wave functions 3313 Andrew Brandt

  8. Pauli Exclusion Principal • Symmetric solution: • Anti-symmetric solution: • Suppose particles are in the same state a=b • Conclude that electrons must have anti-symmetric wave functions since observed to not be in same quantum state • Particles with odd half-integer spin (1/2,3/2,…) like electrons, neutrons, and protons are fermions and obey the PEP and are described by Fermi-Dirac statistics • Spin 0 or integer spin (photons, alpha particles) are symmetric under exchange and do not obey the exclusion principle; these are termed bosons since they follow Bose-Einstein Statistics 3313 Andrew Brandt

  9. Periodic Table • Mendeleev found that elements with similar chemical and physical properties (groups) occur at regular intervals • The organizing of the elements according to their properties into the Periodic Table was a major breakthrough in the history of science • The groups (columns) show similar properties while the intervals are represented by the rows • Read through Ch. 8 for some discussion on the properties of the different elements 3313 Andrew Brandt

  10. Periodic Table 3313 Andrew Brandt

  11. Periodic Table 3313 Andrew Brandt

  12. Deriving Chemistry • The structure of atoms with multiple electrons is determined by two principles • A system is stable when the total energy is minimum • Only one electron at a time is allowed in a particular quantum state • Much can be learned about atomic structure by considering each electron as though it exists in a constant electric field +Ze decreased by the partial screening of the nucleus by electrons that are between the electron under consideration and the nucleus 3313 Andrew Brandt

  13. Atomic Structure Electrons for H and He atoms are in the K shell. H: 1s1 or 1s He: 1s2 Hydrogen: (n, ℓ, mℓ, ms) = (1, 0, 0, ±½) in ground state. • In the absence of a magnetic field, the state ms = ½ is degenerate with the ms = −½ state. Helium: (1, 0, 0, ½) for the first electron. (1, 0, 0, −½) for the second electron. • Electrons have anti-aligned (ms = +½ and ms = −½) spins as being paired. Supports Pauli exclusion principle. • The principle quantum number also has letter codes. • n = 1 2 3 4... • Letter = K L M N… • n = shells (eg: K shell, L shell, etc.) • nℓ = subshells (eg: 1s, 2p, 3d) 3313 Andrew Brandt

  14. Shells and Sub-shells • Electrons with same n roughly at same distance, occupy same shell • n=1 K n=2 L n=3 M n=4 N n=5 O • within each shell there are sub-shells with same angular momentum, small l states are less shielded than big l states, so energy has small increase with l • sodium z=11: 1s2 2s2 2p6 3s1 principal quantum number identifies shell, letter identifies sub-shell, super script is number of electrons in a given subshell • n=1 2 electrons n=2 8 electrons n=3 3s2 3p6 3d10 Ne=2x(2l+1) 18 electrons total electrons in a shell is 2n2 • notion of shells and sub-shells fits perfectly into pattern of periodic table: closed shell electrons are tightly bound (noble gasses), alkali metals have valence electron far from nucleus, easily ionized • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 (transition elements chemical properties determined by 4s electrons) • Hund’s rule parallel spins more separated, energetically favorable leads to ferromagnetism 3313 Andrew Brandt

  15. Consider Sodium 3313 Andrew Brandt

  16. Atomic Structure How many electrons may be in each subshell? Recall: ℓ = 0 1 2 3 4 5 … letter = sp dfgh … ℓ = 0, (s state) can have two electrons. ℓ = 1, (p state) can have six electrons, and so on. The lower ℓ values have more elliptical orbits than the higher ℓ values. Electrons with higher ℓ values are more shielded from the nuclear charge. Electrons lie higher in energy than those with lower ℓ values. 4s fills before 3d. 3313 Andrew Brandt

  17. Groups and Periods Groups: • Vertical columns. • Same number of electrons in an ℓ orbit. • Can form similar chemical bonds. Periods: • Horizontal rows. • Correspond to filling of the subshells. • ionization energies of elements and atomic radii. 3313 Andrew Brandt

  18. The Periodic Table Inert Gases: Last group of the periodic table Closed p subshell except helium Zero net spin and large ionization energy Their atoms interact weakly with each other Alkalis: Single s electron outside an inner core Easily form positive ions with a charge +1e Lowest ionization energies Electrical conductivity is relatively good Alkaline Earths: Two s electrons in outer subshell Largest atomic radii High electrical conductivity 3313 Andrew Brandt

  19. The Periodic Table Halogens: Need one more electron to fill outermost subshell Form strong ionic bonds with the alkalis More stable configurations occur as the p subshell is filled Transition Metals: Three rows of elements in which the 3d, 4d, and 5d are being filled Properties primarily determined by the s electrons, rather than by the d subshell being filled Have d-shell electrons with unpaired spins As the d subshell is filled, the magnetic moments, and the tendency for neighboring atoms to align spins are reduced 3313 Andrew Brandt

  20. The Periodic Table Lanthanides (rare earths): Have the outside 6s2 subshell completed As occurs in the 3d subshell, the electrons in the 4f subshell have unpaired electrons that align themselves The large orbital angular momentum contributes to the large ferromagnetic effects Actinides: Inner subshells are being filled while the 7s2 subshell is complete Difficult to obtain chemical data because they are all radioactive Have longer half-lives 3313 Andrew Brandt

  21. Spin-orbit Coupling 3313 Andrew Brandt

  22. 8.2: Total Angular Momentum Orbital angular momentum Spin angular momentum L, Lz, S, Sz ,J and Jz are quantized. Total angular momentum 3313 Andrew Brandt

  23. Adding Angular Momenta • what is the • total angular • momentum • when I add the • spin angular momentum • of an electron to its • orbital angular momentum? • l=1 +s=1/2? • 3/2? 3313 Andrew Brandt

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