LO 1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data. (Sec 7.12) LO 1.6 The student is able to analyze.

LO 1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data. (Sec 7.12) LO 1.6 The student is able to analyze data relating to electron energies for patterns and relationship. (Sec 7.12) LO 1.7 The student is able to describe the electron structure of the atom, using PES (photoelectron spectroscopy) data, ionization energy data, and/or Coulomb’s Law to construct explanations of how the energies of electrons within shells in atoms vary. (Sec 7.12) LO 1.9 The student is able to predict and/or justify trends in atomic properties based on location on the periodic table and/or the shell model. (Sec ) LO 1.10 Students can justify with evidence the arrangement of the periodic table and can apply periodic properties to chemical reactivity. (Sec ) LO 1.12 The student is able to explain why a given set of data suggests, or does not suggest, the need to refine the atomic model from a classical shell model with the quantum mechanical model. (Sec )

LO 1.13 Given information about a particular model of the atom, the student is able to determine if the model is consistent with specific evidence. (Sec 7.11) LO 1.15 The student can justify the selection of a particular type of spectroscopy to measure properties associated with vibrational or electronic motions of molecules. (Sec 7.1)

AP Learning Objectives, Margin Notes and References
LO 1.15 The student can justify the selection of a particular type of spectroscopy to measure properties associated with vibrational or electronic motions of molecules. Additional AP References LO 1.15 (see APEC #1, “Energy Levels and Electron Transitions”) LO 1.15 (see Appendix 7.4, “Molecular Spectroscopy: An Introduction”)

Different Colored Fireworks
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Electromagnetic Radiation
One of the ways that energy travels through space. Three characteristics: Wavelength Frequency Speed Copyright © Cengage Learning. All rights reserved

Characteristics Wavelength ( ) – distance between two consecutive peaks or troughs in a wave. Frequency ( ) – number of waves (cycles) per second that pass a given point in space Speed (c) – speed of light (2.9979×108 m/s) Copyright © Cengage Learning. All rights reserved

The Nature of Waves

Classification of Electromagnetic Radiation

Energy can be gained or lost only in whole number multiples of A system can transfer energy only in whole quanta (or “packets”). Energy seems to have particulate properties too. Copyright © Cengage Learning. All rights reserved

The Photoelectric effect
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Continuous spectrum (results when white light is passed through a prism) – contains all the wavelengths of visible light Line spectrum – each line corresponds to a discrete wavelength: Hydrogen emission spectrum Copyright © Cengage Learning. All rights reserved

Refraction of White Light

The Line Spectrum of Hydrogen

CONCEPT CHECK! Why is it significant that the color emitted from the hydrogen emission spectrum is not white? How does the emission spectrum support the idea of quantized energy levels? If the levels were not quantized, we’d probably see white light. This is because all possible value of energy could be released, meaning all possible colors would be emitted. All the colors combined make white light. Since only certain colors are observed, this means that only certain energy levels are allowed. An electron can exist at one level or another, and there are regions of zero probability in between. Copyright © Cengage Learning. All rights reserved

LO 1.12 The student is able to explain why a given set of data suggests, or does not suggest, the need to refine the atomic model from a classical shell model with the quantum mechanical model.

Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. Bohr’s model gave hydrogen atom energy levels consistent with the hydrogen emission spectrum. Ground state – lowest possible energy state (n = 1) Copyright © Cengage Learning. All rights reserved

For a single electron transition from one energy level to another: ΔE = change in energy of the atom (energy of the emitted photon) nfinal = integer; final distance from the nucleus ninitial = integer; initial distance from the nucleus Copyright © Cengage Learning. All rights reserved

The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the electron. As the electron becomes more tightly bound, its energy becomes more negative relative to the zero-energy reference state (free electron). As the electron is brought closer to the nucleus, energy is released from the system. Copyright © Cengage Learning. All rights reserved

EXERCISE! What color of light is emitted when an excited electron in the hydrogen atom falls from: n = 5 to n = 2 n = 4 to n = 2 n = 3 to n = 2 Which transition results in the longest wavelength of light? blue, λ = 434 nm green, λ = 486 nm orange/red, λ = 657 nm For each transition, use ΔE = hc / λ = (–2.178×10–18)[(1/nf) – (1/ni)]. Solve for λ in each case. a) blue (λ = 434 nm) b) green (λ = 486 nm) c) orange/red (λ = 657 nm) The longest wavelength of light is from transition n = 3 to n = 2 (letter c). Copyright © Cengage Learning. All rights reserved

LO 1.12 The student is able to explain why a given set of data suggests, or does not suggest, the need to refine the atomic model from a classical shell model with the quantum mechanical model.

We do not know the detailed pathway of an electron. Heisenberg uncertainty principle: There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time. Δx = uncertainty in a particle’s position Δ(mν) = uncertainty in a particle’s momentum h = Planck’s constant Copyright © Cengage Learning. All rights reserved

Physical Meaning of a Wave Function (Ψ)
The square of the function indicates the probability of finding an electron near a particular point in space. Probability distribution – intensity of color is used to indicate the probability value near a given point in space. Copyright © Cengage Learning. All rights reserved

Probability Distribution for the 1s Wave Function

Radial Probability Distribution

Relative Orbital Size Difficult to define precisely. Orbital is a wave function. Picture an orbital as a three-dimensional electron density map. Hydrogen 1s orbital: Radius of the sphere that encloses 90% of the total electron probability. Copyright © Cengage Learning. All rights reserved

Principal quantum number (n) – size and energy of the orbital.
Angular momentum quantum number (l) – shape of atomic orbitals (sometimes called a subshell). Magnetic quantum number (ml) – orientation of the orbital in space relative to the other orbitals in the atom.

Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atom

EXERCISE! For principal quantum level n = 3, determine the number of allowed subshells (different values of l), and give the designation of each. # of allowed subshells = 3 l = 0, 3s l = 1, 3p l = 2, 3d The allowed values of l run from 0 to 2, so the number of allowed subshells is 3. Thus the subshells and their designations are: l = 0, 3s l = 1, 3p l = 2, 3d Copyright © Cengage Learning. All rights reserved

EXERCISE! For l = 2, determine the magnetic quantum numbers (ml) and the number of orbitals. magnetic quantum numbers = –2, – 1, 0, 1, 2 number of orbitals = 5 The magnetic quantum numbers are -2, -1, 0, 1, 2. The number of orbitals is 5. Copyright © Cengage Learning. All rights reserved

LO 1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data. (Sec 7.12) LO 1.6 The student is able to analyze.

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LO 1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data. (Sec 7.12) LO 1.6 The student is able to analyze.

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