HOME

TheInfoList



OR:

The
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
of a material exhibits a strong and fundamental relationship with the nature of radiation interactions within that medium. There are numerous mathematical descriptions of different interaction processes that are dependent on the atomic number, . When dealing with composite media (i.e. a bulk material composed of more than one
element Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of o ...
), one therefore encounters the difficulty of defining . An effective atomic number in this context is equivalent to the atomic number but is used for compounds (e.g. water) and
mixtures In chemistry, a mixture is a material made up of two or more different chemical substances which can be separated by physical method. It is an impure substance made up of 2 or more elements or compounds mechanically mixed together in any proporti ...
of different materials (such as tissue and
bone A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, ...
). This is of most interest in terms of radiation interaction with composite materials. For bulk interaction properties, it can be useful to define an effective atomic number for a composite medium and, depending on the context, this may be done in different ways. Such methods include (i) a simple mass-weighted average, (ii) a
power-law In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity var ...
type method with some (very approximate) relationship to radiation interaction properties or (iii) methods involving calculation based on interaction cross sections. The latter is the most accurate approach (Taylor 2012), and the other more simplified approaches are often inaccurate even when used in a relative fashion for comparing materials. In many textbooks and scientific publications, the following - simplistic and often dubious - sort of method is employed. One such proposed formula for the effective atomic number, , is as follows: Z_\text = \sqrt .94/math> where * f_n is the fraction of the total number of
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s associated with each element, and * Z_n is the atomic number of each element. An example is that of water (H2O), made up of two hydrogen atoms (Z=1) and one oxygen atom (Z=8), the total number of electrons is 1+1+8 = 10, so the fraction of electrons for the two hydrogens is (2/10) and for the one oxygen is (8/10). So the for water is: Z_\text = \sqrt .94= 7.42 The effective atomic number is important for predicting how
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
s interact with a substance, as certain types of photon interactions depend on the atomic number. The exact formula, as well as the exponent 2.94, can depend on the energy range being used. As such, readers are reminded that this approach is of very limited applicability and may be quite misleading. This 'power law' method, while commonly employed, is of questionable appropriateness in contemporary scientific applications within the context of radiation interactions in heterogeneous media. This approach dates back to the late 1930s when photon sources were restricted to low-energy
x-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
units. The exponent of 2.94 relates to an
empirical formula In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, is simply SO, as is the empir ...
for the photoelectric process which incorporates a ‘constant’ of 2.64 × 10−26, which is in fact not a constant but rather a function of the photon energy. A
linear relationship In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
between Z2.94 has been shown for a limited number of compounds for low-energy x-rays, but within the same publication it is shown that many compounds do not lie on the same trendline. As such, for polyenergetic photon sources (in particular, for applications such as
radiotherapy Radiation therapy or radiotherapy (RT, RTx, or XRT) is a treatment using ionizing radiation, generally provided as part of cancer therapy to either kill or control the growth of malignant cells. It is normally delivered by a linear particle ...
), the effective atomic number varies significantly with energy. It is possible to obtain a much more accurate single-valued by weighting against the spectrum of the source. The effective atomic number for electron interactions may be calculated with a similar approach. The cross-section based approach for determining ''Z''eff is obviously much more complicated than the simple power-law approach described above, and this is why freely-available software has been developed for such calculations.


References

{{reflist * Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Atomic physics