- Length: 6 pages
- Subject: Physics
- Type: Term Paper
- Paper: #50477434

*Note*: Sample below may appear distorted but all corresponding word document files contain proper formatting

Quantum mechanics is a theory that has emerged in the study of both chemistry and physics and has been received with a lot of enthusiasm. Nobel laureate physicist Philip Anderson goes as far as naming quantum mechanics the greatest invention of the last 2000 years, describing its impact saying,

The quantum theory forces a revision of our mode of thinking, which is far more profound than Newtonian mechanics or the Copernican revolution or relativity... It tells us that we really completely know the rules of the game which all these particles and quanta are playing, so that if we are clever enough we can understand everything about ourselves and our world. In other words, there is no "why" question about our everyday world that the quantum theory can't answer for is - Why is the sky blue? Why is glass transparent? What holds DNA together? Why does the sun shine? - and so on."

This expresses the potential of quantum mechanics to tie together various fields of study. Since quantum mechanics is about atoms and atoms are the basis of all matter, quantum mechanics has the potential to explain everything. This explains the interest shown in the area of quantum mechanics and the enthusiasm scientists have for studying the field.

It is also important to note that while quantum mechanics is a relatively new area of study, it has its basis in previous areas of study. Quantum mechanics can be seen as the latest addition to a century of scientific study attempting to determine the basis of matter. This begins with the classical theory of the atom, continues to Bohr's simple atomic theory, and develops further with de Broglie's wave theory, Heisenberg's uncertainty principle and Schrdinger's equation. The final result is quantum mechanics as it is known today.

To further investigate the development of quantum mechanics, each of these stages will be looked at in more detail, showing the main ideas that each stage added to the understanding of the atom. This will show that quantum mechanics is based on the combination of the ideas of many scientists, with the final acceptance of quantum theory occurring when Schrodinger's equation tied together previous theories and allowed them to be applied to subatomic particles.

Classical Theory of the Atom

The classical theory of the atom is based on the model of an atom being made up of a positive nucleus containing protons and neutrons with negatively charged electrons orbiting around this nucleus. This model was first proposed by Rutherford in 1911 who described the atom saying, "Most of the volume of the atom is empty space in which electrons move around the nucleus."

This basic model of the atom has been expanded on and used to determine how chemicals react with each other, the charges of chemicals and the physical properties of chemicals. While this has involved expanding the theory, the basic understanding of the structure remains the same.

While many theories look at atoms in much more complex ways, the important characteristics that remain is that electrons orbit the nucleus and that electrons determine the properties of the atom.

Simple Bohr Atomic Theory

Bohr's atomic theory expanded on the work of Rutherford with Bohr focusing on explaining the hydrogen atom, the simplest atom. Bohr accepted the idea that electrons orbit the nucleus of the atom. Applying classical physics to this situation, this would mean the electron would move in a circular path of differing energy, decreasing in energy until the electron crashed into the nucleus. This was a major flaw in Rutherford's theory, as one book explains,

According to classical electromagnetic theory, the atom model of Rutherford would be unstable. The electrons revolving about the nucleus are accelerated charged particles; therefore, they should continuously emit radiation, lose energy, and execute descending spirals until they fall into the positive center."

Bohr's theory did not reject the ideas of classical physics but did assume that the laws of physics did not apply to atoms. To explain how electrons could remain in orbit without crashing into the nucleus Bohr proposed that electrons are quantized. This involved proposing that electrons were only able to exist in orbits of certain radii and certain energy he called allowed energy states. In these allowed energy states, the electrons do not emit energy and so will not lose energy and crash into the nucleus but will remain in this orbit indefinitely.

Bohr's theory also included the idea that electrons were able to move between certain allowed energy states, absorbing or emitting radiation to achieve this move between energy states. Bohr used this theory to explain the spectrum of hydrogen. As one author explains, based on Bohr's theory,

The regularities in the frequencies of the spectral lines is understood; each spectral line arises when electrons change from one allowed orbit to another, and its frequency corresponds to the difference between the two energies."

This theory of Bohr's marks the beginning of a change in understanding the nature of atoms, a change that was a major factor in the development of quantum physics. The major problem with Bohr's theory is that it was only successful in explaining the simplest atom hydrogen, where hydrogen has only one electron. Attempts to explain the next simplest atom helium, having two electrons, were unsuccessful. This was the problem that prompted the next step towards the development of quantum theory.

The Wave Properties of the Electron Proposed by de Broglie

The next stage in the development of quantum mechanics occurred when physicist de Broglie considered Bohr's theory and "made the radical suggestion that a particle has associated with it a wave." De Broglie proposed that matter could have wavelike properties and that the orbit of the electron had a certain wavelength associated with it. De Broglie further proposed that the wavelength of the wave is inversely proportional to the momentum of the particle. This proposal was the first time matter had been treated as if it were a wave and marked a significant step forward in the development of quantum theory.

Uncertainty Principle of Heisenberg

Based on the wave theory developed by de Broglie, Heisenberg formulated the uncertainty principle. This principle was based on complex mathematics and showed that it could be known where an electron was at any time, or where it was heading based on its momentum, but never both.

As one author explains, Heisenberg showed that,

The limitations of the observer did not result from limitations in experimental technique nor or at some imagined future time when those technical restrictions might very well be lifted. Rather, the limitations were imposed by the very nature of the subatomic world itself. It was impossible to measure simultaneously both the precise momentum and the precise position of a subatomic particle."

This principle expressed a limitation that would remain part of quantum theory.

This uncertainty principal went against the ideas of Rutherford and of Bohr, since both their theories had required that electrons be in precise orbits around the nucleus. The uncertainty principle meant that these orbits could never be known, since the properties of an orbit are based on knowing the location of the orbiting body and its momentum. Heisenberg's theory therefore put a hole in the theories of Rutherford and Bohr and called for the development of another theory to effectively explain the movement of electrons in the atom.

Schrdinger's Equation

The work of physicist Erwin Schrdinger provided the theory that explained the movement of electrons within the atom while remaining in agreement with Heisenberg's uncertainty principle. Schrdinger formulated an equation that gave the wave function of a particle. As one text explains,

When the Schrdinger equation is solved for a free particle, it is found that the wavefunction has a wavelength given by the de Broglie relation, and that solutions of the equation exist for any wavelength. However, when the equation is solved for a particle that is confined to a small region of space or is bound to an attractive center (like an electron in an atom), it is found that acceptable solutions can be obtained only for certain energies. That is, the energy of such particles is quantized, or confined to discrete values."

This equation is in agreement with the uncertainty principle because "the solutions to these equations were mathematical functions that described only probabilities, not actualities."

Quantum Mechanics

Schrdinger's equation is often referred to as marking the beginning of quantum mechanics. As has been noted, Schrdinger's equation evolved from a series of previous work. Classical theory proposed that electrons orbited a nucleus and that the electrons were responsible for the properties and reactions of atoms. Bohr proposed that electrons were in specific allowable energy states, with this used to explain why electrons did not spiral and crash into the nucleus as classical physics predicted. De Broglie made a radical suggestion by proposing that electrons might be understood not as particles but as waves. Heisenberg's uncertainty principle showed the error in Bohr's and Rutherford's theories by showing that the position and momentum…[continue]

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