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QUANTUM THEORY

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This is a theory based on using the concept of the quantum unit to describe the dynamic properties of matter and radiation. The foundation was laid by the German physicist Max Planck, who discovered in 1900 that energy can be emitted or absorbed by matter only in small, definite units called quanta. An exciting section of this theory is the uncertainty principle, discovered by the German physicist Werner Heisenberg in 1927, which states that the position and speed of a particle cannot be specified at the same time.

Early History

In the 18th and 19th centuries, Newtonian, or classical, mechanics appeared to provide a wholly accurate description of the motions of bodies—for example, planetary motion. In the late 19th and early 20th centuries, however, many discoveries began to doubt Newton. One of them were the lines that appear in the spectra of light emitted by heated gases, or gases in which electric discharges take place. From the model of the atom developed in the early 20th century, scientists had also expected that the electrons would emit light over a broad frequency (no. of waves per second) range, rather than in the narrow frequency ranges that form the lines in a spectrum.

Another puzzle for physicists was the coexistence of two theories of light: the corpuscular theory, which explains light as a stream of particles, and the wave theory, which views light as electromagnetic waves. A third problem was the absence of a molecular basis for thermodynamics. In his book Elementary Principles in Statistical Mechanics (1902), the American physicist J. Willard Gibbs believed that it was impossible to discover a theory which could explain molecular action, thermodynamics, radiation, and electrical phenomena as they were then understood.

Planck's Introduction of the Quantum

At the turn of the century, physicists did not yet clearly recognize that these and other difficulties in physics were in any way related. The first development that led to the solution of these difficulties was Planck's introduction of the concept of the quantum, as a result of physicists' studies of blackbody radiation. (The term blackbody refers to an ideal body or surface that absorbs all light without any reflection.) A body at a high temperature—a “red heat”—gives off most of its radiation in the low frequency (red and infrared) regions; a body at a higher temperature—“white heat”—gives off more radiation in higher frequencies (yellow, green, or blue). During the 1890s physicists studied these phenomena and expressed their results in a series of curves or graphs. The classical theory predicted an altogether different set of curves from those actually observed. What Planck did was to devise a mathematical formula that described the curves exactly; he then deduced a physical hypothesis that could explain the formula. His hypothesis was that energy is radiated only in quanta of energy hu, where u is the frequency and h is the quantum action, now known as Planck's constant.

Einstein's Contribution

The next important developments in quantum mechanics were the work of German-born American physicist and Nobel laureate Albert Einstein. He used Planck's concept of the quantum to explain the photoelectric effect—a phenomenon in which electrons are emitted from metal surfaces when light falls on these surfaces.

According to classical theory, the energy, as measured by the voltage of the emitted electrons, should be proportional to the intensity (concentration) of the radiation. The energy of the electrons, however, was found to be independent of the intensity of radiation—which determined only the number of electrons emitted—and to depend solely on the frequency of the radiation. The higher the frequency of the incident ("falling") light waves, the greater is the electron energy; below a certain frequency no electrons are emitted. These facts were explained by Einstein by assuming that a single quantum of radiant energy ejects a single electron from the metal. The energy of the quantum is proportional to the frequency, and so the energy of the electron depends on the frequency.

The Bohr Atom

In 1911 Rutherford discovered the atomic nucleus. He assumed, on the basis of experimental evidence, that every atom consists of a dense, positively charged nucleus, surrounded by negatively charged electrons revolving around the nucleus as planets revolve around the sun. The classical electromagnetic theory developed by the British physicist James Clerk Maxwell predicted that an electron revolving around a nucleus will continuously produce light energy until it has lost all its energy, and eventually will fall into the nucleus. Thus, according to classical theory, an atom, as described by Rutherford, can't exist for a long time. This led the Danish physicist Niels Bohr, in 1913, to suggest that in an atom the classical theory does not hold, and that electrons move in fixed orbits. Every change in orbit by the electron corresponds to the absorption or emission of a quantum of radiation.

It was difficult to prove Bohr's theory to atoms with more than one electron. The mathematical equations for the next simplest atom, the helium atom, were solved during the 1910s and 1920s, but the results were not entirely proved by experiment. For more complex atoms, only approximate solutions of the equations are possible, and these don't agree with observations.

Wave Mechanics

The French physicist Louis Victor de Broglie suggested in 1924 that because electromagnetic (light, x-ray, infra-red, etc.) waves can behave like particles, particles should, in some cases, also behave like wave. This prediction was proved within a few years by the American physicists Clinton Joseph Davisson and Lester Halbert Germer and the British physicist George Paget Thomson. They showed that a beam of electrons scattered by a crystal produces a  pattern characteristic of a wave. The wave concept of a particle led the Austrian physicist Erwin Schrödinger to develop a so-called wave equation to describe the wave properties of a particle.

Although this equation was gave solutions for all points in space, the solutions of the equation could only work in certain conditions called eigenfunctions (German eigen, “own”). The Schrodinger wave equation thus had only certain solutions; these solutions were mathematical expressions in which quantum numbers appeared as parameters. (Quantum numbers are integers developed in particle physics to give the size of certain quantities of particles or systems.) The Schrodinger equation was solved for the hydrogen atom and gave conclusions which agreed with earlier quantum theory. Moreover, it was solvable for the helium atom, which earlier theory had failed to explain, and here also it was in agreement with experiments. The solutions of the Schrodinger equation also indicated that no two electrons could have exactly the same amount of energy. This rule is called the exclusion principle.

The Meaning of Quantum Mechanics

Even for the simple hydrogen atom, which consists of two particles, mathematical results are extremely complex. The next simplest atom, helium, has three particles, and even in the simple mathematics of classical dynamics, the three-body problem is not entirely soluble. The energy levels can be calculated accurately, however, even if not exactly. In applying quantum mathematics to complex situations, a physicist can use one of a number of mathematical formulas. The choice depends on the suitable approximate solutions.

Although quantum mechanics describes the atom purely mathematically, a rough description can be given of what the atom is now thought to be like. Surrounding the nucleus is a series of stationary waves; these waves have crests at certain points, each complete standing wave representing an orbit. The absolute square of the amplitude of the wave at any point is a measure of the probability that an electron will be found at that point at any given time. Thus, an electron can no longer be said to be at any precise point at any given time.

The Uncertainty Principle

Heisenberg, in 1927 formulated the uncertainty principle. This principle states that it is impossible to calculate the position and speed of a particle at the same time. In other words, the more accurately a particle's speed is measured and known, the less accuracte the position can be measured. This principle is also fundamental to the understanding of quantum mechanics as it is generally accepted today: The wave and particle character of electromagnetic radiation can be understood as two complementary properties of radiation.

Another way of expressing the uncertainty principle is that the wavelength of a particle or wave increases as the speed and mass decrease. As atoms are cooled they slow down and their wavelength grows larger. At a low enough temperature this wavelength is bigger than the space between the particles, causing atoms to overlap, becoming impossible to tell apart, and melding into a single quantum state. In 1996 a team of Colorado scientists, led by physicist Eric Cornell and University of Colorado physicist Carl Weiman, cooled rubidium atoms to a temperature so low that the particles entered this merged state, known as a Bose-Einstein condensate. This made millions of atoms behave like one atom.