Breakdown, Discussion & Help With Sample Problems: What You Should Know

7.1 The Nature of Light

Figures 7.1-7.3 (p 257) nicely summarize many of the important points within 7.1. CHEM 200 students need to be familiar with terms within 7.1, including as frequency, wavelength, amplitude, the electromagnetic spectrum, the quantum, photoelectric effect and photons.

click here for a few words about SAMPLE PROBLEM 7.1 (page 258)

The take-home message from Section 7.1? The idiosyncratic properties of all electromagnetic radiation (including light) require explanations that invoke aspects of wave as well as aspects of particles.

click here for a few words about SAMPLE PROBLEM 7.2 (page 262)

7.2 Atomic Spectra and the Bohr Model of the Atom

A hydrogen atom (as is the case with all atoms), when vaporized and thermally or electrically excited, emits light that, when dispersed by a prism, produces a line spectrum.

A line spectrum is a series of fine lines of individual colors separated by colorless spaces...and its existence flies in the face of the nuclear model in which electrons orbit nuclei and emit radiation of continuously varying wavelength as they spiral into the nucleus. The observations of the line spectra for hydrogen prodded Niels Bohr into devising his model...which suggests that a spectral line results from the emission of a photon of specific energy when the electron moves from a higher energy state to a lower one. Furthermore, the Bohr model predicts that an atomic spectrum appears as lines rather than as a continuum because the atom energy has only certain discrete levels, or states.

In other words, according to the Bohr model, the different paths that an electron can take, in its travels around the nucleus, can be likened to the orbits that planets take around their sun.

Figure 7.9 (p 264) is a nice depiction of the Bohr model.

7.3 The Wave-Particle Duality of Matter and Energy

The idea that both matter and energy are best described by attributes of waves and particles is proposed and defended in this section.

The wave-particle duality of matter and energy reaches its conclusion with two equations: 7.5--which enables determination of the de Broglie wavelength (l) for all objects (p 270); and 7.6--which is the arithmetic expression for the Heisenberg uncertainty principle (p 273).

l = h/mu                         (7.5)
Dx * mDu   [> than or = to] h/4p        (7.6)

Refer to pages 270 and 273 for additional details about these important equations.

Careful inspection of eq 7.5 reveals that matter behaves as though it was moving in a wave (think about that one!).

A similarly careful analysis of eq 7.6 suggests that it is impossible to know simultaneously the exact position (x) and velocity (u) of a particle.

click here for a few words about SAMPLE PROBLEM 7.4 (page 273)

7.4 The Quantum-Mechanical Model of the Atom

From Silberberg: "The [quantum mechanical] model describes an atom that has certain allowed amounts of energy due to the allowed wave-like motion of an electron whose exact location is impossible to know."

The nuts-and-bolts of Section 7.4, after an initial foundation on pages 274 and 275, is contained within pages 276-281...and includes introductions of the quantum numbers of the atomic orbital: the principal quantum number, the azimuthal quantum number, and the magnetic quantum number.

These three quantum numbers, along with the spin quantum number (Chapter 8), are the tools that CHEM 200 students need to utilize when describing electrons...understanding Table 7.2 (p 277) is a good place to start as far as mastering this subject.

click here for a few words about SAMPLE PROBLEM 7.5 (page 277)

click here for a few words about SAMPLE PROBLEM 7.6 (page 278)

Section 7.4 concludes with nice discussions, and graphics, of s, p, and d orbitals (Figs 7.15, 7.16, and 7.17, respectively).

exercises such as numbers 7.6, 7.45, 7.53, and 7.71 are all straightforward problems of the type that are often found on CHEM 200 exams