Radiation research and mathematics
Radiation research encompasses the study of energy transmission through waves or particles, known as quanta, which can be either beneficial or harmful depending on their source and application. Types of radiation include ionizing radiation, like X-rays and particles from radioactive decay, and nonionizing radiation, such as visible light and radio waves. This field is critical for understanding the effects of radiation on human health and the environment, as well as for developing protective measures against harmful effects. Mathematicians have played a significant role in this research, contributing essential theories and models. Notable figures include Wilhelm Wien and Max Planck, whose work laid the groundwork for quantum theory, and Victor Twersky, known for his expertise in radiation scattering. Current mathematical approaches, including Monte Carlo simulations, are utilized to address challenges in radiation detection and shielding, particularly in space applications. Understanding the properties of radiation, such as wavelength and frequency, is vital for determining its potential impacts and practical uses.
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Radiation research and mathematics
Summary: Radiation research has a heavy mathematical component, especially in modeling distribution of or shielding from radiation.
Radiation is the transmission of energy via waves or particles, such as energetic electrons, photons, or nuclear particles. These waves or particles, called “quanta,” travel radially in all directions from the source, leading to the name “radiation.” Radiation exists everywhere, from both natural sources, like the sun, and many man-made sources, like radio stations and particle accelerators. The various types of radiation that exist may be harmful or beneficial to people, depending on source and application. Ionizing radiation contains enough energy per quantum to detach electrons from atoms, like X-rays or the radiation emitted by particle accelerators. High energy particles are created constantly by all luminous objects in the universe. Most of these particles never reach the surface of Earth. They may be deflected by magnetic fields or interact with atmospheric particles. Common types of nonionizing radiation include visible light, radio waves, and microwaves.
Many mathematicians have contributed to radiation research, like Wilhelm Wien, who derived a distribution law of radiation and won a Nobel Prize for his work on heat radiation. Physicist Max Planck used some of Wein’s mathematics as the basis for quantum theory. Paul Ehrenfest contributed to quantum statistics, in part by applying Plank’s quantum theory to rotating bodies. Subrahmanyan Chandrasekhar won the Royal Society Copley Medal for his work in mathematical astronomy, including the theory of radiation. Victor Twersky was widely regarded as an expert on radiation scattering. His work has been used in diverse applications, such as studying the effect of atmospheric dust on light propagation. Mathematicians continue to work on radiation problems, including applications such as detecting radiation or shielding satellites from the harmful effects of cosmic radiation, as well as creating mathematical methods for formulating and investigating radiation problems, such as Monte Carlo simulations.
Properties
Properties of radiation waves can be used to determine their potential effects on people and objects or their usefulness for applications. Wavelength is the length of one cycle of the wave, or the distance from one peak to the next. Frequency is the number of cycles of the wave that travel past a fixed point along its path per unit time. All electromagnetic waves travel in a vacuum at a speed of about 3×108 meters per second. A fundamental relationship between wavelength and frequency is that wave speed is the product of wavelength and frequency, which means that greater wavelengths correspond to lower frequencies. The energy of electromagnetic photons is the product of wave frequency and Planck’s constant, so higher frequencies produce greater photon energies. Among the common types of EMR radiation, radio waves have the longest wavelengths, resulting in low frequencies and low energies. Higher frequency ultraviolet radiation has the most energy and is the most harmful component of the cosmic radiation that penetrates Earth’s atmosphere. X-rays, discovered by physicist Wilhelm Röntgen, occur naturally when solar wind is trapped by Earth’s magnetic field in the Van Allen belts, named for physicist James Van Allen.
Black holes are also sources of X-rays in the universe. While photons have no mass, some forms of radiation are particles with positive mass produced in the atomic decay of radioactive materials. For example, beta radiation is composed of high-energy electrons, which are dangerous because they can penetrate skin to the layer where new cells are produced. Mathematician Jesse Wilkins’s work on mathematical models to compute the penetration and absorption of electromagnetic gamma rays has been used in the design of nuclear radiation shields.
Bibliography
Dupree, Stephen, and Stanley Fraley. A Monte Carlo Primer: A Practical Approach to Radiation Transport. New York: Springer, 2001.
Knoll, Glenn. Radiation Detection and Measurement. Hoboken, NJ: Wiley, 2010.
U.S. Environmental Protection Agency. “Radiation Protection.” http://www.epa.gov/radiation/programs.html.