Chemistry (Chang), 9th Edition

Chapter 7: Quantum Theory and the Electronic Structure of Atoms

Chapter Summary

1. The quantum theory developed by Planck successfully explains the emission of radiation by heated solids. The quantum theory states that radiant energy is emitted by atoms and molecules in small discrete amounts (quanta), rather than over a continuous range. This behavior is governed by the relationship E = hv, where E is the energy of the radiation, h is Planck’s constant, and v is the frequency of the radiation. Energy is always emitted in whole-number multiples of hv (1 hv, 2 hv, 3 hv, . . .).

2. Using quantum theory, Einstein solved another mystery of physics—the photoelectric effect. Einstein proposed that light can behave like a stream of particles (photons).

3. The line spectrum of hydrogen, yet another mystery to nineteenth-century physicists, was also explained by applying the quantum theory. Bohr developed a model of the hydrogen atom in which the energy of its single electron is quantized—limited to certain energy values determined by an integer, the principal quantum number.

4. An electron in its most stable energy state is said to be in the ground state, and an electron at an energy level higher than its most stable state is said to be in an excited state. In the Bohr model, an electron emits a photon when it drops from a higher-energy state (an excited state) to a lower-energy state (the ground state or another, less excited state). The release of specific amounts of energy in the form of photons accounts for the lines in the hydrogen emission spectrum.

5. De Broglie extended Einstein’s wave-particle description of light to all matter in motion. The wavelength of a moving particle of mass m and velocity u is given by the de Broglie equation λ = h/mu.

6. The Schrödinger equation describes the motions and energies of submicroscopic particles. This equation launched quantum mechanics and a new era in physics.

7. The Schrödinger equation tells us the possible energy states of the electron in a hydrogen atom and the probability of its location in a particular region surrounding the nucleus. These results can be applied with reasonable accuracy to manyelectron atoms.

8. An atomic orbital is a function (ψ) that defines the distribution of electron density (ψ²) in space. Orbitals are represented by electron density diagrams or boundary surface diagrams.

9. Four quantum numbers characterize each electron in an atom: the principal quantum number n identifies the main energy level, or shell, of the orbital; the angular momentum quantum number <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0035715985/117363/7.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a> indicates the shape of the orbital; the magnetic quantum number m specifies the orientation of the orbital in space; and the electron spin quantum number m_s indicates the direction of the electron’s spin on its own axis.

10. The single s orbital for each energy level is spherical and centered on the nucleus. The three p orbitals present at n = 2 and higher; each has two lobes, and the pairs of lobes are arranged at right angles to one another. Starting with n = 3, there are five d orbitals, with more complex shapes and orientations.

11. The energy of the electron in a hydrogen atom is determined solely by its principal quantum number. In many-electron atoms, the principal quantum number and the angular momentum quantum number together determine the energy of an electron.

12. No two electrons in the same atom can have the same four quantum numbers (the Pauli exclusion principle).

13. The most stable arrangement of electrons in a subshell is the one that has the greatest number of parallel spins (Hund’s rule). Atoms with one or more unpaired electron spins are paramagnetic. Atoms in which all electrons are paired are diamagnetic.

14. The Aufbau principle provides the guideline for building up the elements. The periodic table classifies the elements according to their atomic numbers and thus also by the electronic configurations of their atoms.