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## Physics Tutorials

### Birth of Modern Science

in 1864 James Clerk Maxwell proposed that light is an electromagnet wave traveling through an ether. Prior to the 1900's light was generally believed to travel in the form of waves, delivering energy from one location to another smoothly, like waves traveling across the ocean.

Black-body radiation The search for an efficient light bulb stimulated interest in radiation emitted by hot objects. An efficient light bulb is one that emits a lot of light and little heat. Researchers wanted to determine what intensity of light was given off at each wavelength for any particular temperature of a hot object. The apparatus used was called a "blackbody" (or "black body"), which is a box, completely sealed with no doors or windows. The box is heated and radiation emitted from the inner walls, reflecting or absorbing at the walls. A small hole is pierced into one side and the radiation that escapes is measured. Any light entering the hole is absorbed by the "body," and re-emitted with the same characteristics as the rest of the radiation produced by the body. Since the light sent in does not come back, the body appears black.

#### Modernism

In October, 1900 Planck developed a mathematical description of the intensities of wavelengths of light produced by black bodies. His was the first law to fit experimental data. He then attempted to derive the law from basic principles. In his derivation he was forced to propose the idea of energy quanta. He related the energy of the atoms that make up the wall to their frequency of vibration. He proposed the total energy of all the atoms vibrating at a particular frequency was E = hƒ. In other words, atoms could not have any old energy; they could only have an energy that related to their particular frequency of vibration.

In December 1900 Planck presented his findings at a conference. It was pretty much a yawn. It seems no one, including Planck, realized the significance of this proposal. It was interpreted as a mathematical device to fit a curve and nothing more. Planck determined the value of "h." Since then no other fundamental physical constant has been discovered. Planck also found the value of another constant, "k," required for his law. He named it the Boltzmann constant and used it to determine the mass of an atom. Prior to October 1900, Planck was unconvinced that atoms existed.

In 1905 Einstein proposed that light traveled in discreet packets called quanta, like bullets from a machine gun. He interpreted Planck's equation as giving the energy of each quanta. He showed that the radiation bouncing around inside a black body cavity acted like gaseous particles, with each particle having energy, E = hƒ. He generalized this postulate to describe matter absorbing or giving off energy "as if" energy consisted of discrete particles. He made a further refinement in Planck's postulate. Einstein maintained that E = hƒ referred to the energy of each atom in a solid, providing the recognition of quantization of energy in matter as well as in light. Einstein's ideas, published in 1906, were ignored because the concept of "particles" of energy that had "frequency," was completely at odds with the accepted wave theory, and could not be easily understood. Further, light properties such as diffraction and interference were definitely wave-like. Also, Albert Einstein was a newbie.

Einstein developed the photoelectric law in support of his ideas. The photoelectric effect is the emission of electrons from the surface of a metal when light shines on the metal. If energy was absorbed continuously, than any frequency of light shining on the metal for a long enough time should eventually cause electrons to boil off the surface. This is not what happens. Below a certain frequency of light, no electrons are emitted from the surface, no matter how intense the light or for how long the light shines on the surface. Einstein postulated that a single packet of light with sufficient energy (high enough frequency) was what was needed to rip one electron away from the surface. The excess energy contained in higher frequency quanta was absorbed by the electron giving it more kinetic energy.

In 1909 Einstein, by then renowned for his relativity theory, proposed publicly not only that light traveled as particles, but also these quanta had momentum. Relativity theory had rendered the notion of an ether as unnecessary and these energy particles, he proposed, existed on their own, independently of matter.

In 1913, Bohr unveiled his model of atomic structure in which electrons could only exist in certain orbitals, and could only absorb or emit specific quanta of energy that corresponded to differences in allowed energy levels. His model fit emission and absorption spectra of the hydrogen atom.

In 1915 Robert Millikan's study of the photoelectric effect verified Einstein's photoelectric law.

In 1923, Louis de Broglie suggested that if light could have properties of particles, then particles, particularly electrons, could have wave properties. He predicted that the wavelength of a particle is inversely proportional to the momentum of the particle.

In 1924, Arthur Compton published verification of Einstein's assertion of the momentum of quanta. Compton studied the scattering of radiation by electrons. When radiation strikes electrons, the radiation changes direction and frequency. Unaware of Einstein's assertion, Compton first struggled unsuccessfully to explain the effects on the basis of a wave model. He pictured radiation bouncing off electrons in the same way a water wave reflects off a large rock in a pond. He could not explain the change in frequency of the radiation. Then he pictured the radiation and electrons interacting as particles, bouncing off each other like two hockey pucks on an icy surface. In the process, the radiation gave up some of its energy to the electron, coming away with a lower frequency. The mathematical treatment of this concept, invoking E = hƒ, fit the experimental data. The scientific community was finally generally convinced of the existence of the light quantum. Einstein was the first person to predict the existence of a fundamental particle.

In 1926 the American chemist, Gilbert Lewis, published a paper proposing that light is made of atoms which he called "photons." The paper was discredited, but the new name for light quanta stuck.

In 1927 two researchers working independently of each other verified de Broglies' matter waves. Davisson studied electrons passing through metal crystals, and George Paget Thomson shot electrons through metal foils. They found electrons passing between the atoms of a crystal or a foil diffract and produce an interference pattern just as light passing through a slit diffracts and produces an interference pattern. Davisson and Thomson each found the interference pattern produced maxima where de Broglie's equation suggested they would. Electrons were shown to behave as waves.

Planck died in 1947, unconvinced of the existence of photons.

quantum physics problems

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