Radiation, exponential attenuation

Beta radiation has a finite range, whereas in theory x- and gamma rays are exponentially attenuated. It should be noted that x-radiation of each energy exhibits sharp changes in absorption coefficients for certain absorbers. 

The exponential la,w for absorbing radiation energy as given in Eq. (10-1) is not exact for gamma photons, principally because the scattering of some of the photons in the beam and subsequent return is not true adsorption. The attenuation of beam intensity is always less than predicted by Eq. (10-1) and this physical phenomenon is taken into account by modifying the exponential attenuation law to give... 

Exponential attenuation in the case of electromagnetic radiation, a = alpha P = beta X = X-ray... 

Figure 2.3 Impact of ionizing radiation on polymers. (A) Simplified scheme of radiation-induced events in polymers. (B and C) Comparison of the interaction of VVphotons and electrons with polymers. Photon beams are exponentially attenuated along the beam direction, whereas electrons are scattered and slowed down along their path through the polymer fdm. Source Adapted from Drobny [2], with permission from Elsevier Ltd.

Exposure is minimized by ehoiee of souree, by duration of exposure, by distanee from souree (at 1 m die radiation level is redueed almost 10-fold), and by shielding. The greater die mass per unit area of shield material die greater die shielding effieieney. Whereas a- and (3-partieles pose few problems (die former ean be absorbed by, e.g., paper and die latter by 1 em Perspex) y- and X-rays are not eompletely absorbed by shield material but attenuated exponentially sueh dial radiation emerging from die shield is given by ... 

The thickness of a Mossbauer sample affects not only the strength of the Mossbauer signal but also the intensity of the radiation arriving at the detector because the y-rays are inherently attenuated by the sample because of nonresonant mass absorption caused by the photo effect and Compton scattering as mentioned earlier. The counting rate C in the detector decreases exponentially with the density of the absorber,... 

Density, level, and thickness measurements all depend upon the determination of the number of radiations per unit time penetrating the sample and producing a measurable signal in the radiation detector. When the amount of matter between the source and the detector increases, there usually is a decrease in the signal. The following relationship demonstrates the exponential natme of the attenuation of beta oi gamma radiation ... 

Using basic exponential radiation attenuation concepts, this reference shows the development of the expression for determining the hydrogen concn in a piece of mail ... 

Attenuated total reflection FTIR is a well-established technique for obtaining absorbance spectra of opaque samples. The mode of interaction is unique because the probing radiation is propagated in a high index-of-refraction internal reflection element (IRE). The radiation interacts with the material of interest, which is in close contact with the IRE, forming an interface across which a nonpropagating evanescent field penetrates the surface of the material of interest to a depth in the order of one wavelength of the radiation. The electric field at the interface penetrates the rarer medium in the form of an evanescent field whose amplitude decays exponentially with distance into the rarer medium. 

The interaction of ionizing electromagnetic radiation with matter is different from the processes previously mentioned, and the concept of ranges and specific ionization loss cannot be applied. Only the three most important absorption processes are considered the photoelectric effect, the Compton effect, and the pair-production effect. The corpuscular description of electromagnetic radiation is the most appropriate for these effects, as one photon in a well-collimated beam of photons disappears at each interaction. The attenuation of the photon beam can be described by a simple exponential law... 

In ATR-FTIR excitation occurs only in the immediate vicinity of the surface ol the reflection element, in an evanescent wave resulting from total internal reflection. The intensity of the evanescent field decays exponentially in the direction normal to the interface with a penetration depth given by (1.7.10.121, which for IR radiation is of the order of a few hundreds of nm. Absorption leads to an attenuation of the totally reflected beam. The ATR spectrum is similar to the IR transmission spectrum. Only for films with a thickness comparable to, or larger than, the penetration depth of the evanescent field, do the band intensities depend on the film thickness. Information on the orientation of defined structural units can be obtained by measuring the dichroic ratio defined as R = A IA, where A and A are the band absorbances for radiation polarized parallel and perpendicular with respect to the plane of incidence, respectively. From this ratio the second-order parameter of the orientation distribution (eq. [3.7.13]) can be derived ). ATR-FTIR has been extensively used to study the conformation and ordering in LB monolayers, bilayers and multilayers of fatty acids and lipids. Examples of various studies can be found... 

Upon the Ag and In deposition the totally symmetric modes are initially strongly enhanced. Subsequently the signal is attenuated exponentially with an exponent that is much smaller than the penetration depth of the incident radiation in a smooth closed metal film, reflecting a high level of roughness of the metal overlayer. On the other hand, the intensity of the normally infrared active modes relative to the Raman modes provides information on the metal diffusion depth in the organic films. 

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