Atomic Structure • • • • Origin of the elements Structure of atoms ❧ Hydrogen ❧ Others Periodic Trends Synthesis of elements ❧ Big bang 15E9 years ago ❧ Temperature 1E9 K ❧ Upon cooling influence of forces felt ➠ 2 hours * H (89 %) and He (11 %) ➠ Strong force for nucleus ➠ Electromagnetic force for electrons 1-1 1-2 Fundamental Forces 1-3 Subatomic particles • A number of subatomic particles have relevance to chemistry ❧ Electron ❧ Proton ➠ Z, atomic number ❧ Neutron ➠ N, different isotopes of same element * 12C, 13C, 14C ❧ Photon ❧ Neutrino ❧ Positron ❧ α particle ❧ β particle 1-4 1-5 1-6 Origin of element • Initial H and He • Others formed from nuclear reactions ❧ H and He still most abundant 1-7 Origin of elements • Gravitational coalescence of H and He into clouds • Increase in temperature to fusion • Proton reaction ❧ 1H + 1H → 2H + e+ + νe + 0.42 MeV • CNO cycle ❧ 12C + 1H →13N + γ ❧ 13N →13C + e+ + νe ❧ 13C + 1H →14N + γ ❧ 14N + 1H →15O + γ ❧ 15O →15N + e+ + νe ❧ 15N + 1H →12C + 4He ❧ Net result is conversion of 4 protons to alpha particle ➠ 4 1H → 4He +2 e++ 2 νe +3 γ 1-8 Origin of elements He burning ❧ 4He + 4He ↔ 8Be + γ - 91.78 keV ❧ 8Be + 4He → 12C + γ + 7.367 MeV Neutron Capture and proton emission ❧ 14N + n →14C +1H; 14N(n,1H)14C Neutron Capture; S-process ❧ 68Zn(n, γ) 69Zn ❧ 69Zn → 69Ga + β− + ν • R process ❧ nuclei are bombarded with a large neutron flux ❧ form highly unstable neutron rich nuclei ❧ rapidly decay to form stable neutron rich nuclei • P process ❧ Proton capture, not as common 1-9 Origin of elements • Binding energy ❧ Difference between energy of nucleus and nucleons ➠ Related to mass excess * ∆m=mnucleonsmnucleus * Ebind=∆mc2 ➘ Related to nuclear models 1-10 Origin of elements • How is Au formed from Ir? ❧ Start with 193Ir and base on s process ➠ 193Ir + n->194Ir + β-->194Pt ➠ 194Pt + 3n ->197Pt + β- ->197Au * Relies upon nuclear process 1-11 Periodic property of element • Common properties of elements ❧ Medeleev • Modern period table develop ❧ Actinides added in 1940s by Seaborg ❧ s, p, d, f blocks 1-12 Hydrogenic atoms • Atoms with only one electron ❧ Simplifies calculations ➠ Electron position described by wavefunction ψ * x, y, z, and time * Probability of finding electron in a space proportional to ψ2 2 ψ ∫ dτ = 1 1-13 Orbitals • Wavefunctions specified by quantum numbers ❧ n=1,2,3,4 ➠ Principal quantum number ❧ l=0 to n-1 ➠ Orbital angular momentum ➠ Electron orbitals * s,p,d,f ❧ ml= +l ❧ Spin=+-1/2 ➠ Energy related to Z and n * ∆Etrans=kZ2∆(1/n2) 1-14 Distribution of electrons 1-15 Bohr Atom • Models of atoms ❧ Plum pudding ❧ Bohr atom ➠ Inclusion of quantum states ➠ Based on Rutherford atom • Bohr atom for 1 electron system ❧ Etotal =1/2mev2+q1q2/4πεοr ➠ q2=-e * Include proton and electron ❧ 1/2mev2-Ze2/4πεοr 1-16 Bohr Atom • Net force on the electron is zero ❧ 0=Fdynamic+Fcoulombic ❧ 1/2mev2/r+q1q2/4πεοr2 ➠ Force is 1/r2E = ∫ Fdr ➠ Energy 1/r ❧ 1/2mev2/r-Ze2/4πεοr2 ➠ Z is charge on nucleus • Quantize energy through angular momentum ❧ mvr=nh/2π, n=1,2,3…. ➠ Can solve for r, E, v 1-17 Bohr radius • R=(εοh2/πmee2)(n2/Z) ❧Radius is quantized and goes at n2 ❧R=0.529 Å for Z=1, n=1 ➠ Ao (Bohr radius) 1-18 Atomic Spectra • Quantum numbers ❧n=1,2,3,4 ❧r=aon2/Z for gases with 1 electron • Energy ❧E=-(mee4/8εο2h2)Z2/n2 ❧For ground state H ➠ E=2.18E-18 J/atom=k * Can determine J/mole 1312 kJ/mole ➠ Energy goes as –k/n2 * System converges to limit 1-19 Energy • n=infinity, r=infinity , E=0, unbound e• Ionization energy ❧k is ionization energy • Velocity ❧v=nh/2πmer • Ionization energy ❧Minimum energy required to remove electron from atom in gas phase ➠ Multiple ionization energies 1-20 Balmer states • Gas H in tube ❧Four lines in visible region ❧Fit lines • 1/λ=(1/22-1/n2)R, R=1.1E-7 m-1 ❧1/λ=ν (wavenumber) ❧E=1/2mev2=eV (V=Volts) ➠ At 1 V = 1.6E-19 J =eV ➠ K=13.6 eV 1-21 Matter energy interaction • Eincident=1/2mv2=qV • Escattered ❧∆E =Eincident-Escattered ❧∆E=kZ2(1/n2final-1/n2in)=hν=hc/λ ❧De-excitation of electron results in photon emission ➠ Corresponds to line emission 1-22 Orbitals 1-23 Many Electron Atoms • Electron configuration ❧ Based on quantum numbers ❧ Pauli exclusion principle ❧ Aufbau principle and Hund’s rule ➠ Degenerate orbitals have same spin ➠ Maximize unfilled orbitals * 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 1-24 Many electron obitals • Electron configuration of Zr and Zr4+ ❧ [Kr]4d25s2 and [Kr] • For Fe, Fe2+, and Fe3+ ❧ [Ar]4s23d6, [Ar]4s23d4, [Ar]4s23d3 • Effective nuclear charge ❧ Zeff=Z-σ ➠ Related to electron penetration towards nucleus 1-25 Effective Nuclear Charge y = m1 + m2 * M0 y = m1 + m2 * M0 Value m1 20 m2 Chisq R effective charge 15 Error -1.4319 0.30333 0.74935 0.022984 0.22715 NA 0.99812 NA m1 Data m21 Chisq R Value -0.080608 Error 0.060699 0.97519 0.027228 0.99994 0.0049655 NA NA y = m1 + m2 * M0 Value m1 m2 10 Chisq R Error -5.53 0.24075 0.741 0.015874 0.01008 NA 0.99954 NA 5 0 0 5 10 15 1s 2s 3s 20 1-26 Z Atomic Radii • Increase down a group • Decrease across a period ❧ Lanthanide and actinide contraction 1-27 Ionic Radius 1-28 1-29 Orbital energies (MJ/mole) H Li C F Na Si Cl K Ca Sc Ti V Br 1s 2s 2p 3s 3p 3d 4s 4p -1.31 -6.26 -0.52 E ~ -(Zeff)2/n -28.34 -1.88 -1.04 -67.18 -3.87 -1.80 -104.19 -6.82 -3.67 -0.50 -183.58 -15.09 -10.24 -1.44 -0.75 -273.46 -26.64 -20.08 -2.44 -1.33 -349.83 -37.00 -29.13 -3.94 -2.38 -0.42 -390.90 -43.04 -34.25 -4.86 -3.15 -0.59 -434.47 -48.95 -39.37 -5.51 -3.41 -0.77 -0.72 -480.40 -55.11 -44.61 -6.30 -3.81 -0.89 -0.68 -528.69 -61.54 -50.26 -6.95 -4.20 -0.97 -0.72 -1303.01 -172.82 -151.69 -26.11 -18.11 -7.35 -2.36 -1.22 1-30 1-31 Ionization energy • Energy needed to remove electron ❧ Depends upon quantum state ❧ Ranked by electron configuration ➠ Measured in eV * 1 eV= 96.485 kJ/mol 1-32 Electron Affinity • Enthalpy gain when a gas phase atom gains an electron 1-33 Electronegativity 1-34