Book cover for College Physics

College Physics

Eugenia Etkina, Michael Gentle, Alan Van Heuvelen

ISBN #9780321715357

1st Edition

2,258 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section traces the evolution of atomic models from early classical ideas to the modern quantum mechanical understanding. Starting with the Bohr model and its quantized orbits, students learn how specific energy levels relate to photon emission and absorption. The introduction of quantum numbers (n, l, m?, and m?) through experiments such as the Zeeman effect and the Davisson-Germer experiment provides deeper insight into electron configurations and the structure of the periodic table. The sections on de Broglie waves, the uncertainty principle, and quantum tunneling underscore the wave–particle duality that governs microscopic systems, leading to practical applications such as lasers.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

The electron in a hydrogen atom spends most of its time $0.53 \times 10^{-10} \mathrm{m}$ from the nucleus, whose radius is about $0.88 \times 10^{-15} \mathrm{m} .$ If each dimension of this atom was increased by the same factor and the radius of the nucleus was increased to the size of a tennis ball, how from the nucleus would the electron be?

Example 2

A single layer of gold atoms lies on a table. The radius of each gold atom is about $1.5 \times 10^{-10} \mathrm{m},$ and the radius of each gold nucleus is about $7 \times 10^{-15} \mathrm{m} .$ A particle much smaller than the nucleus is shot at the layer of gold atoms. Roughly, what is its chance of hitting a nucleus and being scattered? (The electrons around the atom have no effect.)

Example 3

(a) Determine the mass of a gold foil that is 0.010 $\mathrm{cm}$ thick and whose area is 1 $\mathrm{cm} \times 1 \mathrm{cm} .$ The density of gold is $19,300 \mathrm{kg} / \mathrm{m}^{3} .$ (b) Determine the number of gold atoms in the foil if the mass of each atom is $3.27 \times 10^{-25} \mathrm{kg} .(\mathrm{c})$ The radius of a gold nucleus is $7 \times 10^{-15} \mathrm{m} .$ Determine the area of a circle with this radius. (d) Determine the chance that an alpha particle passing through the gold foil will hit a gold nucleus. Ignore the alpha particle's size and assume that all gold nuclei are exposed to it; that is, no gold nuclei are hidden behind other nuclei.

Example 4

An object of mass $M$ moving at speed $v_{0}$ has a direct elastic collision with a second object of mass $m$ that is at rest. Using the energy and momentum conservation principles (Chapters 5 and 6 ), show that the final velocity of the object of mass $M$ is $v=(M-m) v_{0} /(M+m) .$ Using this result, determine the final velocity of an alpha particle following a head-on collision with (a) an electron at rest and (b) a gold nucleus at rest. The alpha particle's velocity before the collision is 0.010$c$ $m_{\mathrm{alpha}}=6.6 \times 10^{-27} \mathrm{kg} ; \quad m_{\mathrm{electron}}=9.11 \times 10^{-31} \mathrm{kg} ; \quad$ and $m_{\mathrm{gold} \text { nucleus }}=3.3 \times 10^{-25} \mathrm{kg} .(\mathrm{c})$ Based on your answers, could an alpha particle be deflected backward by hitting an electron in a gold atom?

Example 5

Describe what happens to the energy of the atom and represent your reasoning with an energy bar chart when (a) a hydrogen atom emits a photon and (b) a hydrogen atom absorbs a photon.
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