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Ch. 8 The Quantum Mechanical Atom

Ch. 8 The Quantum Mechanical Atom. Brady & Senese, 5th Ed. Index. 7.1. Electromagnetic radiation provides the clue to the electronic structures of atoms 7.2. Atomic line spectra are evidence that electrons in atoms have quantized energies

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Ch. 8 The Quantum Mechanical Atom

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  1. Ch. 8 The Quantum Mechanical Atom Brady & Senese, 5th Ed.

  2. Index 7.1. Electromagnetic radiation provides the clue to the electronic structures of atoms 7.2. Atomic line spectra are evidence that electrons in atoms have quantized energies 7.3. Electrons have properties of both particles and waves 7.4. Electron spin affects the distribution of electrons among orbitals in atoms 7.5. The ground state electron configuration is the lowest energy distribution of electrons among orbitals 7.6. Electron configurations explain the structure of the periodic table 7.7. Quantum theory predicts the shapes of atomic orbitals 7.8. Atomic properties correlate with an atom's electron configuration

  3. Light Acts As A Wave • Wavelength (λ)–the distance light travels to complete one cycle • Frequency (ν) – the number of wave cycles in one second • units are cycles per second (cps) also known as Hertz (Hz) • Hz = s-1 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  4. Frequency And Wavelength Are Related • Note that as the frequency of the wave increases, the wavelength decreases • Regardless of the frequency, light travels at the same speed, c • c=λ×ν • the speed of light (c) = 2.99792458 × 108 m/s • Learning Check: If the frequency of a radio station is 300. MHz, what is the wavelength in m? 0.999 m 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  5. Radiant Energy Spectrum 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  6. Photoelectric Effect (Particle Theory Of Light) • Albert Einstein (1905) E=hν • Shining light on a clean metal surface may eject electrons • There is a threshold energy needed (a work function specific to the metal) • Increasing intensity does not cause the effect • Increasing the frequency of the light does • Conclusions: • Light is composed of “packets” or “particles” of energy known as photons • The energy of each photon is directly proportional to its frequency 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  7. λ 7 x 10-7 m λ 3.2 x 10-7 m Energy And Light Waves • The energy of a wave is proportional to the wave frequency, E=hν • h= Planck’s constant, 6.626 × 10-34 J•s/photon • Learning Check: Why is ultraviolet light (320 nm) more damaging to tissue than a red light (700 nm)? Use energies to make your case. E320 = 6.2×10-19 J E700 = 3×10-19 J Red light UV light 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  8. Your Turn! Which is the correct energy associated with a photon of light with a wavelength of 450 nm? • 6.7×10-4 J • 4.4×10-19 J • 4.4×10-28 J • 6.7×105 J • none of these 7.1 Electromagnetic radiation provides the clue to the electronic structures of atoms

  9. Atomic Emission • Elements exhibit a characteristic color spectrum when heated in an intense flame or via electric arc 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  10. Atomic Emission Spectra • It was found that these elements also emitted light outside of the visible spectrum • Hydrogen is the simplest atom so its emission spectrum was explained first 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  11. Patterns In Atomic Line Spectra • For the hydrogen spectrum, a mathematical pattern was noted and reported using the Balmer-Rydberg equation • n1and n2 are positive integers , where n1 <n2 • Rydberg constant, RH, is an empirical constant=109,678 cm-1 • If n1=1, lines called “Lyman series” (UV) • If n1=2, called “Balmer series” (Visible) • If n1 = 3 called “Paschen series” (IR) • Emitted light is quantized 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  12. Learning Check • What is the wavelength, in m, of light observed from a transition from n=4 to n=2? • What is n2 if the photon undergoes transition to n=2 and the emitted light has a wavelength of 6505Å? 486.272 m n=3 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  13. Your Turn! What energy is expected for the Balmer emission line that starts at n=5? • 2.3×104 J • 4.6×10-23 J • 4.6×10-21 J • None of these 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  14. The Quantum Mechanical Staircase? • Electrons may only possess discrete quantities of energy rather than an infinite range of quantities • Think staircase rather than ramp

  15. The Bohr explanation of the three series of spectral lines.

  16. Bohr’s Model Of The Atom (1913) • Electrons move around the nucleus in fixed paths or orbits much like the planets move around the sun • Orbit positions, labeled with the integer n, have specific potential energy • The lowest energy state of an atom is called the ground state (an electron with n = 1 for a hydrogen atom) 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  17. Absorption And Emission • Electrons that absorb energy are raised to a higher energy level • A particular frequency of light is emitted when an electron falls to a lower energy level 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  18. Bohr’s Model Fails • Theory was not able to explain the spectra of atoms with more than one electron • Theory doesn’t explain the collapsing atom paradox 7.2 Atomic line spectra are evidence that electrons in atoms have quantized energies

  19. Diffraction And Interference • Constructive interference: waves “in-phase” increase amplitude (they add) • Destructive interference: waves “out-of-phase” decrease amplitude (they cancel out) 7.3 Electrons have properties of both particles and waves

  20. x-ray diffraction of aluminum foil electron diffraction of aluminum foil Electrons Exhibit Interference!! • Electrons exhibit certain wave-like behaviors 7.3 Electrons have properties of both particles and waves

  21. Your Turn! Which of the following is evidence that the electrons in an atom act as a wave ? • the emission spectrum is quantized • electrons cannot collapse into the nucleus • electrons diffract • none of these 7.3 Electrons have properties of both particles and waves

  22. Waves are Quantized • Standing waves are produced when a wave is able to resonate in a space (like a guitar string) • Only certain wavelengths fit properly into a given space • Only certain electron wavelengths fit into a given atom 7.3 Electrons have properties of both particles and waves

  23. Standing Waves • The waves created by guitar strings are those for which a half-wavelength is repeated exactly a whole number of times • For a strength of length L with n, an integer, this can be written as: • Wavelengths are quantized! 7.3 Electrons have properties of both particles and waves

  24. The Electron On A Wire- Uniting The Theories • Particle: the kinetic energy of the moving electron is E=½ mv2 • Standing wave, the half-wavelength must occur an integer number of times along the wire’s length n(λ/2)=L • de Broglie’s equation provides the link between these. • m=mass of particle • v= velocity of particle • Combining these relationships: 7.3 Electrons have properties of both particles and waves

  25. de Broglie Explains Quantized Energy • Electron energy is quantized - it depends on the integer n • Energy level spacing (and spectra) changes when electron confinement changes • Lowest energy allowed is for n=1 (the energy cannot be zero, hence atom cannot collapse) 7.3 Electrons have properties of both particles and waves

  26. Wave Functions • Wave that corresponds to the electron is called a wave function • Wave functions for an electron are calledorbitals • Amplitude of the wave function at a given point can be related to the probability of finding the electron there • According to quantum mechanics there are regions of the wire where the electrons will not be found, called nodes 7.3 Electrons have properties of both particles and waves

  27. Quantum Numbers Are a shorthand to describe characteristics of an electron’s position and to predict its behavior • n = principal quantum number. All orbitals with the same principle quantum number are in the same shell • l = secondary quantum number which divides the orbitals in a shell into smaller groups called subshells • ml= magnetic quantum number which divides the subshells into individual orbitals 7.3 Electrons have properties of both particles and waves

  28. Quantum Numbers: What Do They Mean? • n = roughly describes a distance of the electrons from the nucleus. • designated by integers: 1, 2, 3, 4, 5, 6, … • l = describes the shape of the orbitals. • range from 0 to n-1 • designated with numbers : 0, 1, 2, 3, 4, 5…… • or with letters: s, p, d, f, g, h • ml=describes the spatial orientation of the orbital. • designated by numbers specific to the particular orbital • range from –l to +l 7.3 Electrons have properties of both particles and waves

  29. -2 -1 0 +1 +2 -1 0 +1 0 How Do Quantum Numbers Relate to Each Other? 4 d 5 p 5 s p 4 d 3 4 s Energy 3 s 3 p p 2 s 2 • n • l • ml s 1 7.3 Electrons have properties of both particles and waves

  30. Electrons Behave Like Tiny Magnets • Electrons within atoms interact with a magnet field in one of two ways: • clockwise (spin up) • anti-clockwise (spin down) • This gives rise to the spin quantum number, ms • allowed values: + 1/2 or –1/2 7.4 Electron spin affects the distribution of electrons among orbitals in atoms

  31. Pauli Exclusion Principle • No two electrons in the same atom can have identical values for all four quantum numbers • electrons can occupy the same orbital only if they have opposite spin are paired (called diamagnetic) • Substances with more spin in one direction are said to contain unpaired electrons (called paramagnetic) 7.4 Electron spin affects the distribution of electrons among orbitals in atoms

  32. Your Turn! Which is not a possible set of quantum numbers for an electron? 7.5 The ground state electron configuration is the lowest energy distribution of electrons among orbitals

  33. Ground StateElectron Arrangements • Electron configurations list the subshells that contain electrons and indicate their electron population with a superscript • Orbital diagrams-represent each orbital with a circle (or box) and use arrows to indicate the spin of each electron 7.5 The ground state electron configuration is the lowest energy distribution of electrons among orbitals

  34. Arranging Electrons into Subshells and Orbitals • Electrons are placed in the orbitals closest to the nucleus first • Each orbital may hold up to 2 electrons • Electrons fill a sublevel by occupying each orbital individually, then by pairing if needed. This reduces the repulsion between electrons. • Convention shows the first electron in an orbital as spinning “up” • Electrons in the same orbital must spin opposite directions. 7.5 The ground state electron configuration is the lowest energy distribution of electrons among orbitals

  35. AID TO REMEMBER SUBSHELL FILLING ORDER The diagram provides a compact way to remember the subshell filling order. The correct order is given by following the arrows from top tobottom of the diagram, going from the arrow tail to the head, and then from the next tail to the head, etc. The maximum number of electrons each subshell can hold must also be remembered: s subshells can hold 2, p subshells can hold 6, d subshells can hold 10, and f subshells can hold 14.

  36. Electron Occupancy And The Periodic Table The periodic table is divided into regions of 2, 6, 10, and 14 columns corresponding to the maximum number of electrons in s, p, d, and f sublevels 7.6 Electron configurations explain the structure of the periodic table

  37. Sublevels and the periodic table. Each row (period) represents an energy level Each region of the chart represents a different type of sublevel 7.6 Electron configurations explain the structure of the periodic table

  38. Electronic Classification • Valence e-: are in the highest energy level outside the noble gas core. Involved in bonding. • (Inner) Core e-: the e- in the inner energy levels • Noble Gas or Abbreviated Configuration: a short-hand method for writing e- configuration where some or all of the core e- are represented as a noble gas. • Pseudo-valence e- : are outside the noble gas core in lower energy levels • contribute to shielding • occasionally take part in bonding 7.6 Electron configurations explain the structure of the periodic table

  39. Exceptions to the electronic configurations Following the rules for Cr and Cu using noble gas notation we expect the following* [Ar] 3d5 4s1 [Ar] 3d10 4s1 7.6 Electron configurations explain the structure of the periodic table

  40. PROBLEM: Using the periodic table on the inside cover of the text (not Figure 8.12 or Table 8.4), give the full and condensed electrons configurations, partial orbital diagrams showing valence electrons, and number of inner electrons for the following elements: full configuration condensed configuration partial orbital diagram 4s1 3d 4p SAMPLE PROBLEM 8.2 Determining Electron Configuration (a) potassium (K: Z = 19) (b) molybdenum (Mo: Z = 42) (c) lead (Pb: Z = 82) PLAN: Use the atomic number for the number of electrons and the periodic table for the order of filling for electron orbitals. Condensed configurations consist of the preceding noble gas and outer electrons. SOLUTION: (a) for K (Z = 19) 1s22s22p63s23p64s1 [Ar] 4s1 There are 18 inner electrons.

  41. full configuration condensed configuration partial orbital diagram 5s1 4d5 full configuration condensed configuration partial orbital diagram 5p 6s2 6p2 SAMPLE PROBLEM 8.2 continued (b) for Mo (Z = 42) 1s22s22p63s23p64s23d104p65s14d5 [Kr] 5s14d5 There are 36 inner electrons and 6 valence electrons. (c) for Pb (Z = 82) 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p2 [Xe] 6s24f145d106p2 There are 78 inner electrons and 4 valence electrons.

  42. The Effect of Nuclear Charge (Zeffective) The Effect of Electron Repulsions (Shielding) Factors Affecting Atomic Orbital Energies Higher nuclear charge lowers orbital energy (stabilizes the system) by increasing nucleus-electron attractions. Additional electron in the same orbital An additional electron raises the orbital energy through electron-electron repulsions. Additional electrons in inner orbitals Inner electrons shield outer electrons more effectively than do electrons in the same sublevel.

  43. Figure 8.3 The effect of nuclear charge on orbital energy.

  44. Figure 8.4 Shielding

  45. Figure 8.15 Atomic radii of the main-group and transition elements.

  46. Periodicity of atomic radius Figure 8.16

  47. PROBLEM: Using only the periodic table (not Figure 8.15)m rank each set of main group elements in order of decreasing atomic size: SAMPLE PROBLEM 8.3 Ranking Elements by Atomic Size (a) Ca, Mg, Sr (b) K, Ga, Ca (c) Br, Rb, Kr (d) Sr, Ca, Rb PLAN: Elements in the same group increase in size and you go down; elements decrease in size as you go across a period. SOLUTION: (a) Sr > Ca > Mg These elements are in Group 2A(2). (b) K > Ca > Ga These elements are in Period 4. (c) Rb > Br > Kr Rb has a higher energy level and is far to the left. Br is to the left of Kr. (d) Rb > Sr > Ca Ca is one energy level smaller than Rb and Sr. Rb is to the left of Sr.

  48. Periodicity of first ionization energy (IE1) Figure 8.17

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