Multi-electron atoms & the periodic table

Transcription

1 Lecture 3 Multi-electron atoms & the periodic table Suggested reading: Chapter 1 Journal article is posted online!

2 Goal: Understanding chemical diversity Diamond Graphite Silicon Indium tin oxide Aluminum Cuprate ceramic en.wikipedia.org (carbon, aluminum, superconductor); Edwards group, Oxford (ITO)

3 Recap from last class: Hydrogenic atoms Schrodinger equation: 2 2m m 2 E V 0 Potential of a 1-electron atom: V ( r ) Z eff e 4 r o 2 Electron wavefunctions: ( r,, ) R ( r ) Y (, ) ( n, l l, m l R: Radial wavefunction depends dp d on two quantum numbers, n and l Y: Angular wavefunction depends on another quantum number, m l (A fourth quantum number, also in Y, arises from relativity: m s )

4 Quantum Numbers ( r,, ) R ( r ) Y (, ) ( n, l l, m l n Principal quantum number n = 1, 2, 3, Quantizes the electron energy K, L, M, shells of 1-electron atoms l Orbital angular momentum quantum number l = 0, 1, 2, (n-1) s, p, d, subshells Quantizes the magnitude of orbital angular momentum L m l Magnetic quantum m l = 0, ±1, ±2, ±l number Quantizes the orbital angular momentum along a magnetic field B m s Spin magnetic quantum number m s = ±½ Quantizes the spin angular momentum along a magnetic field B m s : Arises from relativistic quantum theory

5 Quantum Numbers: Shells & subshells

6 n Quantizes the electron energies Knowing ψ, we can use the Schrodinger equation to find the electron energies of 1-electron atoms. E n 4 Z 2 me Z 2 o 2 8 h n (Z is atomic number, n is the quantum number, 1,2,3, ) Ionization energy of hydrogen: energy required to remove the electron from the ground state in the H-atom E I me J 2 2 o h ev

7 Electron energies of Hydrogen Energies are more closely spaced for higher n

8 Energy transitions can occur via photons Absorption of a photon Emission of a photon

9 Example: Solar Spectrum 1829: Josef von Fraunhofer λ dark1 =656.3 nm λ dark2 =486.1 nm E n 2 4 Z me h n o 2 1 E1 ( ) 2 n Convenient conversion: λ [ev]= /λ [nm]

10 Example: Solar Spectrum 1829: Josef von Fraunhofer λ dark1 =656.3 nm λ dark2 =486.1 nm E 3 -E 2 = -13.6[(1/3 2 ) -(1/2 2 )]=1.89eV = 656 nm E 4 -E 2 = 486 nm E n 2 4 Z me h n o 2 1 E1 ( ) 2 n

11 l Quantizes the orbital motion of the electron Obi Orbital angular momentum L 1 1 / 2 ( = 0, 1, 2,.n1) Orbital angular momentum along an applied magnetic field B z L z m

12 l Quantizes the orbital motion of the electron Obi Orbital angular momentum L 1 1 / 2 ( = 0, 1, 2,.n1) Orbital angular momentum along an applied magnetic field B z L z m

13 l Quantizes the orbital motion of the electron Obi Orbital angular momentum L 1 1 / 2 ( = 0, 1, 2,.n1) Orbital angular momentum along an applied magnetic field B z L z m

14 l Quantizes the orbital motion of the electron Obi Orbital angular momentum L 1 1 / 2 ( = 0, 1, 2,.n1) Orbital angular momentum along an applied magnetic field B z L z m = 2

15 s Quantizes the spin momentum of the electron Spin angular momentum 1/ 2 S s s 1 s 1 2 Spin along a magnetic field S m s m z s 1 2

16 s Quantizes the spin momentum of the electron Spin angular momentum 1/ 2 S s s 1 s 1 2 Spin along a magnetic field S m s m z s 1 2

17 Magnetic behavior arises from L and S Orbital magnetic moment e μ L orbital 2m e Spin magnetic moment μ spin e m e S Orbiting/spinning electron is analogous to a current loop (classical magnetic moment μ = current I*area A)

18 Towards multi-electron atoms: Helium (Z=2) Potential energy of one electron in the He atom V ( r, 1 r 12 ) 2 2 2e e 4 r 4 r o 1 o 12 r 12 makes the Schrodinger equation non-separable: can only solve with approximate techniques (not covered in this class)

19 The Orbital Approximation Assume each electron in a multi-electron atom occupies an atomic orbital that resembles those found in hydrogenic atoms. Basically, reducing a many-electron problem to many oneelectron problems (and treating the electron-electron interaction term as a small perturbation) The charge experienced by each electron is the effective nuclear charge Z eff e= (Z-σ)e: Shielding constant σ S l i f th i f th l t i lti l t t Solving for the energies of the electrons in multielectron atoms yields a dependence on n and

20 Energy Usually, the order of energy levels in a shell is s<p<d<f n

21 Atomic orbital energies versus atomic number Z For Z 21, 4s is lower in energy than 3d p d s

22 Effective nuclear charge Z eff First 3 groups of the periodic table Z eff decreases for frontier orbitals and also increases across a period, down a group

23 How do electrons fill these energies? Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers If electrons are in the same orbital (with identical n,, m ), their spins will pair. n=2 n=1 H He Li Be B

24 How do electrons fill these energies? n=2 n=1 Hund s Rule: Experimental spectroscopic studies indicate that electrons in the same n, orbitals prefer their spins to be parallel (same m s ) Origin: If electrons enter the same m by pairing their spin, they will occupy the same spatial distribution (ψ n,,m, ) and experience a strong repulsion C O F

25 Important exceptions to these rules 1. Electron repulsion modifies the atomic orbital trends for elements with an incomplete d-shell. Electrons in such elements first occupy orbitals predicted to be higher in energy (i.e., 4s instead of 3d) General trend: [X]3d n 4s 2 However, all d-block cations and complexes have d n configurations 2. Because electrons with the same ψ n,,m experience a strong repulsion, half-filled fll shells of electrons with parallel spins are particularly stable (spin correlation) Ground state of Cr: [Ar]3d 5 4s 1 or [Ar]3d 4 4s 2

26 Ground State electron configuration of Ti Click for answer

27 Ground State electron configuration of Ti [Ar]3d 2 4s 2

28 Ground State electron configuration of Ti 3+ Click for answer

29 Ground State electron configuration of Ti 3+ [Ar]3d 1

30 Periodic Table Trends In general 1. Metals combine with nonmetals to give hard, nonvolatile solids 2. Nonmetals combine with each other to form volatile molecular l compounds 3. Metals combine with metals to give alloys Columns = groups Rows = periods

31 Rare earths: not as rare as you think! Rare earths: Ce is 26 th most abundant element

32 Lanthanoids Term rare earth refers to hiding behind each other in minearls First discovered lanthanoid, Lanthanum, was found in a cerium mineral All contain 4f-shell electrons, except Lanthanum (which is a d-block element) All form trivalent cations: Ln 3+ All Lanthanoid ions are fluorescent, as a result of the forbidden nature of f-f transitions

33 Applications of Lanthanoids Europium-doped Yttrium vanadate was the first red phosphor to enable the development of color tv screens Lanthanoids deflect UV and IR radiation: used in production of sunglass lenses Lasers, fiber amplifiers, transmission links for internet Amplification & upconversion rticle/tech/41882 First color tv broadcast in 1953 From WebMD: Erbium laser resurfacing is designed to remove superficial and moderately deep lines and wrinkles on the face hands, neck, or chest.

34 Actinoids All are man-made made, except for thorium and uranium All are radioactive First synthesized as part of the Manhattan project in 1944 Some have electrons in 6d orbitals, but in compounds the 6s electrons and any d electrons are lost, leaving the ions with an electronic configuration [Rn]5fn Need particle colliders, nuclear reactors, or supernova for their synthesis A pellet of 238PuO 2 to be used in a radioisotope thermoelectric generator for either the Cassini or Galileo mission. The pellet produces 62 watts of heat and glows because of the heat generated by the radioactive decay (primarily α). ) Photo is taken after insulating the pellet under a graphite blanket for minutes and removing the blanket. (from Wikipedia)

35 Blocks of the Periodic Table

36 S-Block Except for H and He, electrons are easily lost for form positive ions He is exceedingly stable and has no known stable compounds All other s-block elements are very powerful reducing agents never occur naturally in the free state The metallic forms of these elements can only be extracted by electrolysis of a molten salt (Sir Humphry Davy) All are fire hazards and show be stored in Ar React vigorously with H 2 O to liberate hydrogen (Mg, Li, and Be react relatively slowly)

37 Halogens: part of the p-block Highly reactive: found in the environment only as compounds or ions Only periodic table group that contains elements in all 3 states of matter: F and Cl: gases, Br: liquid; I and Astatine, solids F is one of the most reactive elements, attacking otherwise inter materials like glass and forming compounds with the heavier noble gases. Once is does react, the resulting molecule is very inert. Teflon: F+C Hydrogen halides form a series of very strong acids

38 Noble Gases: part of the p-block Odorless Odorless, colorless, monatomic gases Non-flammable, Low chemical reactivity: Ne < He < Ar< Kr < Xe< Rn First noble gas compounds: XeF 4 and XeF 2 (used to etch Si)

39 d-block Co Cr Ni Cu Mn Partly filled d-shell results in unique qualities: 1 Formation of compounds and complexes whose color is due to 1. Formation of compounds and complexes whose color is due to d-d transitions 2. Formation of compounds in many oxidation states, due to low reactivity of unpaired d-electrons 3. Formation of many paramagnetic compounds

40 Trend 1: Effective Nuclear Charge The net positive charge experienced by an electron in a multielectron atom (shielding prevents outermost electrons from feeling full nuclear charge) ge clear charg fective nuc Eff Effective nuclear charge

41 Trend 2: Atomic Radius The distance from the nucleus to the outermost stable electron orbital (here in pm). Increases down a group due to addition of a new energy shell. Decreases across a period because effective nuclear charge increases, attracting electrons

42 Trend 2: Atomic Radius The distance from the nucleus to the outermost stable electron orbital (here in pm). Increases down a group due to addition of a new energy shell. Decreases across a period because effective nuclear charge increases, attracting electrons

43 Trend 3: Ionization Energy The minimum energy required to remove one electron from each The minimum energy required to remove one electron from each atom in a mole of atoms in the gaseous state.

44 Trend 4: Electron affinity and electronegativity Electron affinity: the energy change when a gas-phase atom gains an electron Electronegativity: the ability of an atom to attract electrons when it is g y y part of a compound

45 Polarizability α Ability of an atom to be distorted by an electric field Polarizability is high if the separation of frontier orbitals is small Large, highly hl charged anions are easily polarized Cations that do not have noble-gas configurations are easily polarized Small, highly charged cations easily distort the electron distribution of neighboring ions: strong polarizing ability

46 Trend 5: Metallic character of the elements

47 Trend Summary Metallic character Ionization energy Ato omic radius Effective nuclear cha arge Electron affinity & electronegativity Ioni ization ene ergy Effective nuclear charge Atomic radius