Atomic Orbitals and Quantum Numbers

2. Atomic Orbitals and Quantum Numbers

3. Fundamental particles • When solids, liquids, or gases are heated under pressure they release a continuous spectrum of light. Conversely gases under low pressure emit energy only at specific wavelengths. Each line in the spectra is related to a particular frequency of light emitted by the atoms and each element has a unique emission spectrum. Based on this the German physicist Max Planck proposed that atoms and molecules cannot absorb or emit any arbitrary amount of radiant energy, but only specific quantities. The name quantum was given to these small bundles of energy.

4. Fundamental particles (continued) • Based on Planck’s work, Albert Einstein explained the photoelectric effect, in which light striking metals eject electrons as long as the frequency of the light is above a threshold frequency. This was not in accordance with wave theory, but particle theory explained it quite reasonably. Thus, Einstein proposed that light was composed of a stream of particles he called photons. He conjectured that each photon possesses an energy E equal to the equation E=hv and with a high enough frequency will be able to knock lose an electron.

5. Fundamental particles (continued) • In 1913 Niel's Bohr was able to explain the hydrogen-atom line spectrum by hypothesizing that the single electron of the hydrogen atom can circle the nucleus only in allowed orbits. An electron in any of these paths has a definite amount of energy. The spectrum is produced when an electron drops from a higher orbit to a lower one emitting a photon. To further explain the quantum model of the atom French chemist Louis de Broglie stated that, like light, electrons also exhibit a wave-particle nature. Electrons can be considered as waves confined in a given space around a nucleus. In 1926 the Swiss physicist Erwin Schrodinger formulated wave equations to explain the nature of electron waves. Schrodinger’s model describes general orbital clouds in which electrons may be found based on probability.

6. Heisenberg’s Uncertainty Principle 1927 • An electron orbital describes a region of space around the nucleus in which an electron is most likely to be found, and can be considered as the wave function of an electron in an atom. These orbits as suggested by Schrodinger in his equations can be described using three “quantum numbers”. They are defined as the distance from the nucleus, the orbital shape, and the orbital position in respect to the X, Y, and Z axes. In addition there is a fourth quantum number called the spin quantum number. This is based on the fact that each electron spins either clockwise or counter-clockwise creating a small magnetic field. Each electron in an atom is assigned a set of values for its four quantum numbers that determine the orbital in which it will be found – its address.

7. The Pauli Exclusion Principle • The quantum numbers plus its spin provide an electron’s distinct address. This principle was explained by the Austrian physicist Wolfgang Pauli in his principle that states that no two different electrons in an atom can have the same four quantum numbers. Knowledge of these numbers will decide the electron configuration of an atom.

8. Electron Configurations

9. Discussion Questions • What is the Octet Rule? • What is Hund’s Law? • What is Aufbau? • What is the Pauli Exclusion Principle? • What is electronegativity? • What is electron affinity? • What is ionization energy? • How does the size of atoms change as you move across the periodic table? • Why? • How does the size of atoms change as you move down the periodic table? • Why?