Материал: Андрианова English Thesaurus of Student-Physicist 2013

Blackbody radiation and Planck's hypothesis

An object at any temperature emits electromagnetic radiation, called thermal radiation. The spectrum of the radiation depends on the temperature and properties of the object. At low temperatures, the wavelengths of the thermal radiation are mainly in the infrared region and hence not observable by the eye. As the temperature of an object increases, the object eventually begins to glow red. At sufficiently high temperatures, it appears to be white, as in the glow of the hot tungsten filament of a light-bulb. A careful study of thermal radiation shows that it consists of a continuous distribution of wavelengths from the infrared, visible, and ultraviolet portions of the spectrum.

By the end of the 19th century, it had become apparent that the classical theory of thermal radiation was inadequate. The basic problem was in understanding the observed distribution energy as a function of wavelength in the radiation emitted by a blackbody. By definition, a blackbody is an ideal system that absorbs all radiation incident on it. The radiated energy varies with wavelength and temperature. As the temperature of the blackbody increases, the total amount of energy it emits increases. Also, with increasing temperature, the peak of the distribution shifts to shorter wavelengths. This shift obeys called Wien's displacement law. At long wavelengths, classical theory is in good agreement with the experimental data. At short wavelengths, however, major disagreement exists between classical theory and experiment. In fact, the theory erroneously predicts that the intensity should be infinite, when the experimental data shows it should approach zero. This contradiction is called the ultraviolet catastrophe, because theory and experiment disagree strongly in the short-wavelength, ultraviolet region of the spectrum.

In 1900 Planck developed a formula for blackbody radiation that was in complete agreement with experiments at all wavelengths. Planck hypothesized that blackbody radiation was produced by submicroscopic charged oscillators, which he called resonators. He assumed that the walls of a glowing cavity were composed of billions of these resonators, although their exact nature was unknown. Because the energy of each resonator can have only discrete values, we say the energy is quantized.

The key point in Planck's theory is the assumption of quantized energy states. This is a radical departure from classical physics, the "quantum leap" that led to a totally new understanding of nature. It's shocking: it's

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like saying a pitched baseball can have only a fixed number of different speeds, and no speeds in between those fixed values. When Planck presented his theory, most scientists (including Planck!) didn't consider the quantum concept to be realistic; however, subsequent developments showed that a theory based on the quantum concept (rather than on classical concepts) had to be used to explain a number of other phenomena at the atomic level.

Photoelectric effect and the particle theory of light

In the latter part of the 19th century, experiments showed that light incident on certain metallic surfaces caused the emission of electrons are emitted from the surfaces. This phenomenon is known as the photoelectric effect, and the emitted electrons are called photoelectrons. The first discovery of this phenomenon was made by Hertz, who was also the first to produce the electromagnetic waves predicted by Maxwell.

A successful explanation of the photoelectric effect was given by Einstein in 1905, the same year he published his special theory of relativity. As part of a general paper on electromagnetic radiation, for which he received the Nobel Prize in 1921, Einstein extended Planck's concept of quantization to electromagnetic waves. He suggested that a tiny packet of light energy or photon would be emitted when a quantized oscillator made a jump from an energy state to the next lower state. The work function, which represents the minimum energy with which an electron is bound in the metal, is on the order of a few electron volts.

X- rays

In 1895 at the University of Wurzburg, Wilhelm Roentgen (1845-1923) was studying electrical discharges in low-pressure gases when he noticed that a fluorescent screen glowed even when placed several meters from the gas discharge tube and even when black cardboard was placed between the tube and the screen. He concluded that the effect was caused by a mysterious type of radiation, which he called x-rays because of their unknown nature. Subsequent study showed that these rays traveled at or near the speed of light and that they couldn't be deflected by either electric or magnetic fields. This last fact indicated that x-rays did not consist of beams of charged particles, although the possibility that they were beams of uncharged particles remained.

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Fig. 27. Thesaurus for Unit 27

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In 1912 Max von Laue (1879-1960) suggested that if x-rays were electromagnetic waves with very short wavelengths, it should be possible to diffract them by using the regular atomic spacings of a crystal lattice as a diffraction grating, just as visible light is diffracted by a ruled grating. X-ray diffraction has proved to be an invaluable technique for understanding the structure of matter. The continuous radiation is sometimes called bremsstrahlung, a German word meaning "braking radiation," because electrons emit radiation when they undergo an acceleration inside the target.

The Compton - effect

Further justification for the photon nature of light came from an experiment conducted by Arthur H. Compton in 1923. In his experiment, Compton directed an x-ray beam of wavelength toward a block of graphite. He found that the scattered x-rays had a slightly longer wavelength than the incident x-rays, and hence the energies of the scattered rays were lower. The amount of energy reduction depended on the angle at which the x- rays were scattered. The change in wavelength between a scattered x-ray and an incident x-ray is called the Compton shift.

The dual nature of light and matter

Phenomena such as the photoelectric effect and the Compton effect offer evidence that when light (or other forms of electromagnetic radiation) and matter interact, the light behaves as if it were composed of particles having energy and momentum. In other contexts, however, light acts like a wave, exhibiting interference and diffraction effects. Light has a dual nature, exhibiting both wave and particle characteristics.

According to de Broglie, electrons, just like light, have a dual particlewave nature. De Broglie suggested that all material particles with momentum p should have a characteristic wavelength. Further, de Broglie postulated that the frequencies of matter waves (waves associated with particles having nonzero rest energy) obey the Einstein relationship for photons.

In 1927, three years after de Broglie published his work, C. J. Davisson (1881-1958) and L. H. Germer (1896-1971) of the United States succeeded in measuring the wavelength of electrons. Their important discovery provided the first experimental confirmation of the matter waves proposed by de Broglie.

Wave function

In 1926, the Austrian-German physicist Erwin Schrodinger proposed a wave equation that described how matter waves change in space and

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time. The Schrodinger wave equation represents a key element in the theory of quantum mechanics. It's as important in quantum mechanics as Newton's laws in classical mechanics. Schrodinger's equation has been successfully applied to the hydrogen atom and to many other microscopic systems.

Uncertainty principle

In 1927, Werner Heisenberg (1901-1976) introduced notion, which is now known as the uncertainty principle. It is physically impossible to measure simultaneously the exact position and exact linear momentum of a particle.

The scanning tunneling microscope

One of the basic phenomena of quantum mechanics - tunneling - is at the heart of a very practical device - the scanning tunneling microscope, or STM - which enables us to get highly detailed images of surfaces with a resolution comparable to the size of a single atom. The STM has, however, one serious limitation: it depends on electrical conductivity of the sample and the tip. A newer microscope - the atomic force microscope, or AFM - overcomes this limitation. It measures the force between a tip and the sample, rather than an electrical current. The AFM has comparable sensitivity for measuring topography and has become widely used for technological applications.

1.What phenomena classical physics can’t explain?

2.What kinds of radiation does thermal radiation compose?

3.What’s the essence of Planck's hypothesis?

4.Describe the photoelectric effect.

5.Why x-rays do not consist of beams of charged particles?

6.What’s the reason of dual nature of light?

Exercises

1. Rearrange the letters in the anagrams to form equivalents for the Russian words:

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