Working through this chapter of the study guide will enable you to:

1. Understand why a new theory known as the "dual nature of light" was required to explain the fact that light sometimes must be depicted as a wave and sometimes as a particle.
2. Show how the particle theory of light was used by Niels Bohr to explain the structure of the atom and the emission line spectra produced by gas-discharge tubes.
3. See how the quantum aspects of electromagnetic radiation led to the explanation of line emission spectra and to the development of microwave ovens, lasers, and modern X-ray tubes.
4. Follow the extension of the concept that electromagnetic waves must sometimes be explained as particles to the idea that particles, such as electrons, can sometimes exhibit wavelike properties.

Discussion

Classical physics, as developed by Newton and other great scientists, was able to explain nearly all of the experiments that were being performed around 1900. There was, therefore, a general feeling that nothing really new would ever again be discovered in the area of physics. The few experiments that defied classical explanation, however, opened the door to a vast new realm of study that is now collectively called modern physics. The first lesson to be learned from this chapter is that we should never become too complacent in our knowledge of the world around us. Nature is very complex, and we can be completely sure that we will never grasp all of the aspects of her intricate structure.

Modern physics deals with very small entities, such as the individual component particles in an atom. It is not surprising that a complete understanding of this area of physics was not possible until experimental techniques reached a level that allowed the detailed study of these submicroscopic entities. The real surprise turned out to be that the nature of these submicroscopic particles followed laws much different from the ones that explained everyday interactions in the macroscopic world around us.

Light proved to be an important key in unlocking this intriguing new area of study. It had been known for many years that very hot objects emit light and other types of electromagnetic radiation, but the observed distribution of energy for this radiation did not fit the classical theory. It was necessary to take a bold new approach to the study of light, in which its wave nature was somehow supplemented by a particle (quantum) explanation. This was first proposed by Max Planck in his analysis of the energy distribution in incandescent light spectra, but it was not generally accepted by other scientists until it was shown to be an important part of Einstein's explanation of the photoelectric effect.

From there, the photon (light quantum) concept went on to explain the mystery of the emission and absorption lines that had been baffling scientists in spectroscopy for years. It also showed why the quantum structure of atoms leads to an explanation of the chemical properties of all the elements. Niels Bohr's brilliant formulation of a comprehensive model for the hydrogen atom made all of this possible, and opened the door for the development of practical devices based on the quantum aspects of the atom, such as the laser, the microwave oven, and the modern X-ray tube.

Perhaps the most unexpected consequence of the quantum nature of light was that not only does a wave sometimes require a particle explanation, but entities that had been considered strictly as particles, such as electrons or protons, sometimes require a wavelike description to explain their experimental interactions. The dual nature of light was extended by Louis de Broglie to include the dual nature of particles as well.

Remember that evidence of the modern quantum theory of matter can be seen only on the submicroscopic scale and is not usually apparent in our daily lives. Most of our everyday activities such as throwing a ball or driving a car are still explained very well by classical Newtonian ideas. Today's technical society does, however, rely heavily on some of the subtle aspects of quantum physics, and our understanding of nature cannot be complete unless we include the study of these concepts in our physical science course. Let's move on then to the realm of the atom and see how these new concepts of modern physics help us to better understand the world around us.


Section  9.1Early Concepts of the Atom

In order to understand the structure of matter, scientists have tried to determine the basic building blocks of all material substances for many years. It has always been an attractive idea to define the basic structure of anything and then to build on this structure to develop a solid understanding of the more complex concepts involved in the overall framework of the world and, for that matter, the entire universe.

The concept of the atom was introduced by several early Greek philosophers as the smallest subdivision into which a pure substance could be split. This idea persisted for many years but was finally modified because it could not explain the presence of electrons in all matter as discovered by J. J. Thomson in 1897. After this, various models for the atom were proposed such as Thomson's plum pudding model and finally Rutherford's nuclear model, each of which incorporated the latest scientific data as it became available. The current model of the atom will be described in the next several chapters as we gain the information necessary to understand the basic ideas behind its simple but elegant structure.


Section  9.2The Dual Nature of Light

Whenever good experimental technique produces data that cannot be explained by current theories, scientists grow nervous and eventually someone figures out a way to explain the new data. Usually it only takes some minor refinements to the old ideas or, at most, a slightly different approach. In the case of the spectrum of electromagnetic frequencies emitted by very hot objects, however, minor adjustments to accepted theories did not help. Not until 1900, when Max Planck tried some mathematical "tricks," did a theory emerge that fully explained this experimental anomaly.

No one, not even Planck himself, thought that there was any real physical significance to his new ideas that explained light as a quantum, or bundle, of energy rather than as a traditional wave. Even though his theory fit the data perfectly, it was still thought of only as an innovative mathematical manipulation. Then Albert Einstein came along.

Einstein used the mathematical formulation proposed by Planck to explain an entirely different physical process in which the data from experimental observations did not fit the accepted theories. This process is called the photoelectric effect. In this experiment, light interacts with a clean metal surface to "kick off" electrons in definite, reproducible ways that could be explained only by using Planck's quantum theory.

From that time on, light has been thought of as behaving in a way that requires both wave theory and quantum (particle) theory for a complete explanation. The choice of which one of these theories to use in any given situation depends on the type of experiment being performed. This dual nature of light is at first glance quite strange, but it has proved indispensable in understanding many widely different types of experiments involving light. Light really is quite complex and must be considered sometimes as a wave and sometimes as a particle.

The quanta, or photons, described by Einstein and Planck are not simply random bundles of energy. They are very specific bundles that have definite energies (E ) directly related to the frequency (f ) of the light under study. Planck is credited with developing the following relationship, so the constant (h ) involved in this equation is named after him.

E = hf
where h is Planck's constant and has the value of 6.63 x 10^-34 J-s. This equation shows that even when we must deal with light as a particle, its energy is determined by its frequency, which is a definite wave characteristic.


Section  9.3Bohr Theory of the Hydrogen Atom

From Planck's basic quantum concept, in 1913 Niels Bohr went on to explain another experimental mystery involving the emission lines produced by excited gas samples. Starting from the idea of Rutherford's basic atomic model, Bohr developed a theory showing that the frequencies of the observed emission lines are related to the energy differences between the specific energy levels of the orbits occupied by the electron in a hydrogen atom. The electron's exact energy in each allowed orbit could then in turn be calculated using the quantum ideas of Planck.

Bohr's prediction, that emission lines from hot gases resulted from the changing of electrons from one allowed energy level in an atom to another, matched experimental data perfectly and forever changed the way that we envision the basic structure of the atom. From his theory Bohr was also able to calculate the physical size of an atom and the exact energies of the electron orbits. The lowest energy electron level in an atom is said to be the ground state. The higher energy levels are called excited states.


Section  9.4Microwave Ovens, X-rays, and Lasers

Further study allowed the expansion of the original quantum theory to include absorption lines in the spectrum of white light that had passed through cool gases, and also the production of X-rays, microwaves, and other types of electromagnetic radiation outside of the visible range. Another interesting outcome of quantum theory was the development of a plan to build a special type of light source that took advantage of these same changes in quantized electron energy levels, but this time through a stimulated emission process. This new light source, called the laser, has opened many new technological doors, such as those leading to the making of holograms and to the development of new communication and entertainment systems in widespread use today.


Section  9.5Heisenberg's Uncertainty Principle

Another result of the extremely small size of subatomic particles such as electrons, and the way that we must interact with such particles when we perform measurements on them, is the fact that we can no longer hope to make these measurements with unlimited precision. The uncertainty that is introduced into such measurements was first described by Werner Heisenberg in 1927 and is now expressed in the form of a physical principle bearing his name. The Heisenberg uncertainty principle states that it is impossible to simultaneously know a subatomic particle's exact position and velocity. This uncertainty is related to Planck's constant and places a limit on the precision to which measurements of the properties of subatomic-size particles can be made.


Section  9.6Matter Waves

Perhaps the most unexpected consequence of quantum theory is that not only does a wave sometimes require a particle explanation, but entities that had been considered strictly as particles, such as electrons and protons, now require a wavelike description to explain some of their experimental interactions. The dual nature of light was extended in 1925 by Louis de Broglie to include the dual nature of matter. The study of the wave properties of particles led to the development of an extremely useful experimental tool, the electron microscope, which can be used to view extremely small physical specimens. De Broglie's work also changed the way that we think about basic measurements.

Continued work in quantum theory fostered the concept of a wave equation first developed by Erwin Schrödinger in 1926. The wave function derived from this equation shows us that there are natural limits on how accurately the position and momentum of a subatomic particle such as an electron can be measured simultaneously. The Heisenberg uncertainty principle establishes the limits on such measurements and sheds an entirely different light on the idea of data acquisition in small-scale processes. The concepts described so far in this Section have been combined into quantum mechanics, a branch of physics based on the dual wave and particle behavior of light and matter.


Section  9.7The Quantum Mechanical Model of the Atom

The success of the Bohr theory of the atom, based on a single quantum number (n), was a good beginning for the new quantum mechanical theory, but most scientists were not satisfied. Bohr's theory worked only for single-electron atoms such as hydrogen.

Recall that De Broglie's hypothesis indicated that moving particles have a wave nature, and this idea was confirmed by subsequent experiments. The solution to the problem of the multielectron atoms came in 1926 when Erwin Schrödinger developed the quantum mechanical model (also called the wave mechanical model or the electron cloud model) of the atom. This model focuses on the wave nature of the electron and treats it as a standing wave in orbit around the nucleus (see Figure 9.23 in the textbook). The energy levels are a consequence of the wave having to have a whole number of wavelengths to fit into a stable orbit.

The quantum mechanical model of the atom is more difficult to visualize than the Bohr model. The location of the electron is treated in terms of probabilty (hence the term electron cloud model). However, the quantum mechanical model enables the energies of the electrons in multielectron atoms to be determined accurately, which the Bohr model could not do. Knowing the energies of the electrons is more important than knowing their precise locations. Be sure to examine the chapter's Spotlight feature to understand how our model of the atom has progressed as new information became available.

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