ch231hchapter8

Chapter 8.  Quantum Mechanics and Atomic Structure

A.  Material on Exam II.

1. You know the core behavior of electromagnetic radiation:  its wave behavior, its speed in a vacuum (c = 2.998 x 10¹⁰ cm/s), the relationship between wavelength and frequency (in Hz), the effect of constructive and destructive interference when two waves interact.
2. You know that atoms exhibit emission of radiation at specific discrete wavelengths (and that they absorb radiation at those same discrete energies).  
3. You understand that this discrete behavior led to the development of the Planck equation (E = hν), and the concept that light is quantized with each quantum having a specific energy.
4. You understand the explanation of atomic spectra: that absorption of a photon promotes an electron from a low-energy state to a higher-energy state and that emission of a photon involves the reverse.
5. You know the consequence of this explanation:  that electrons in an atom each have specific (quantized) energies.  
6. You understand the Bohr model of the hydrogen atom and how it explains the atomic spectra of the hydrogen atom.
7. You understand the wave-particle duality of matter, as expressed in the deBroglie equation:  λ = h/(mv).  You understand the impact this has on the behavior of a (very small-mass) electron moving at high velocities.
8. You know that the behavior of an electron can be described by a wave function; and you understand the core concept that an electron behaving as a standing wave around a nucleus leads to a stable situation.

B.  Material after Exam II.

1. You know general form of the Schrodinger equation (Hψ = Eψ), associating a specific energy with every electron in an atom.
2. You know the nature of the four different quantum numbers for electrons in atoms:
   • The principal quantum number n (similar to the energy levels of the Bohr model).
   • The angular momentum quantum number l, that translates to spatial distribution.
   • The magnetic quantum number m_l, which can range from -l to +l
   • The electron spin.
3. You know that each electron in an atom will have a unique collection of quantum numbers, and therefore, a unique energy (excepting that electrons of opposite spin but other equal quantum numbers have the same energies).
4. You understand that the wave function arising from any collection of quantum numbers has both a radial component, and an angular component.  You also know that the mathematical square of any wavefunction provides a spatial probability function for where the electron with that energy will be.
5. You can recognize the angular distributions associated with l = 0 (s), 1 (p) and 2 (d) orbital wavefunctions.
6. You understand that a multielectron atom has all of its electrons simultaneously superimposed; no two electrons ever occupy the same space at the same time, but the wavefunctions (and thus, probability functions) overlap.  The motion of each electron has an impact on every other electron, making analytical solution of the Schrodinger equation impossible for all but 1-electon systems (H, He⁺, Li⁺⁺, etc).  However, close approximations are possible, and the orbitals in a hydrogen atom give a good conceptual picture of more complex systems.
7. You can use the Aufbau process to deduce the necessary quantum numbers for electrons in any atom, and arrive at an electron configuration.
8. You recognize the small number of "anomalous" configurations arizing from half-filled shells.
9. You can express electron configurations fully, or in abbreviated form using noble gas designations.

Links:

Solar spectrum with Fraunhofer lines

The Balmer series of lines for the hydrogen atom spectrum (Wikipedia)

The Lyman series of lines for the hydrogen atom spectrum (Wikipedia)

The "Orbitron"

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