1 v {\displaystyle I=I_{0}e^{-x/\ell }} m The attenuation coefficient of the screen is 23 m-1, and the energy absorption coefficient is 5 m-1. The measured values are compared with the theoretical ones obtained by Seltzer (1993). The measurement unit was used for the mass attenuation coefficient cm2g-1. The mu/rho values are taken from the current photon interaction database at the National Institute of Standards and Technology, and the mu(en)/rho values are based on the new calculations by Seltzer described in Radiation Research. Note that the treatment here also refers to the attenuation of X-rays since, as we noted before gamma-rays and X-rays are essentially the same physical entities. {\displaystyle v} Tables and graphs of computed photon mass attenuation coefficients and mass energy-absorption coefficients from 1keV to 20MeV are presented for all of the elements (Z=1to92) and for 48 compounds and mixtures of radiological interest. Corrections are included for in-flight positron annihilation, previously not applied in NIST calculations for energies above 10 MeV. Corrections are included for in-flight positron annihilation, previously not applied in NIST calculations for energies above 10 MeV. Expressing this more formally we can say that for thicknesses from x = 0 to any other thickness x, the radiation intensity will decrease from I0 to Ix, so that: This final expression tells us that the radiation intensity will decrease in an exponential fashion with the thickness of the absorber with the rate of decrease being controlled by the Linear Attenuation Coefficient. The tables cover energies of the photon (x ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV. {\displaystyle {\overline {\mathbf {v} _{1}\cdot \mathbf {v} _{2}}}=0} , a value directly related to electrical conductivity, that is: where q is the charge, The following equation can then describe the attenuation of X-rays: I=I0.e- (/).l , where is the material density, (/) is the mass attenuation coefficient, and .l is the mass thickness. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. v is the pressure of the gas and This is a relatively large thickness, and it is caused by small atomic numbers of hydrogen and oxygen. Co; 1st edition, 1965. It includes Photo-electric effect, Compton scatter, Coherent scatter, Attenuation of Monochromatic & Polychromatic radiation, Diagnostic Xray applications, Scatter radiations. In X-ray radiography the calculation of the mean free path is more complicated, because photons are not mono-energetic, but have some distribution of energies called a spectrum. 2 2 In this study, total mass attenuation coefficient (/) values in the energy range from 60 keV to 15 MeV for some contrast agents (Iopamidol, Metrizamide, Iohexol, Ioxaglic acid, Iopromide,. Share sensitive information only on official, secure websites. Mass extinction coefficient is an old term for this quantity. The variation is less than this for high-energy radiation beams and in most cases can be ignored. c If, on the other hand, the beam particle is part of an established equilibrium with identical particles, then the square of relative velocity is: v t The following table lists some typical values for air at different pressures at room temperature. is the absolute temperature. The elements covered include Z=10, neon to Z=100, fermium. J. H. Hubbell How much water shielding do you require if you want to reduce the intensity of a 500 keV monoenergetic gamma-ray beam (narrow beam) to 1% of its incident intensity? A locked padlock Gamma ray attenuation is a concept used for the approximate calculation of radiation shielding. The half-value layer for 500 keV gamma rays in water is 7.15 cm, and the linear attenuation coefficient for 500 keV gamma rays in water is 0.097 cm-1. In the kinetic theory of gases, the mean free path of a particle, such as a molecule, is the average distance the particle travels between collisions with other moving particles. [10], This relation is used in the derivation of the Sabine equation in acoustics, using a geometrical approximation of sound propagation.[11]. The Fermi velocity can easily be derived from the Fermi energy via the non-relativistic kinetic energy equation. The effect is greater for high atomic materials such as bone, where the range of variation of (mu-bar/sub en//rho)/sup bone//sub water/, again for cobalt radiation, may be as great as 15%. (2000) ISBN: 9780819477729 -, Fourier transform and Nyquist sampling theorem. hZko7+`fa'klXi@yb*qs9IFM z8|9$*I %:H$" - At. Mass Attenuation Coefficient (MAC): The higher the mass attenuation coefficient, the higher the protection ability of glass. A locked padlock Turning the proportionality in this equation into an equality, we can write: where the constant of proportionality, , is called the Linear Attenuation Coefficient. Standard deviation of the maximum errors in the measured values is calculated to be <2%. e v ISBN-13: 978-3527411764. by Hubbell in the International Journal of Applied Radiation and Isotopes. / The following equation can then describe the attenuation of gamma radiation. The Specific Gamma Ray Constant for 137Cs is 3.3 R hr-1 mCi-1 at 1 cm. So you will not have to plod your way through any new maths below, just a different application of the same form of mathematical analysis! $@\q oF `ic@ D$c |A, 2" '3` C The problem is quite simple and can be described by the following equation: If the half-value layer for water is 4.15 cm, the linear attenuation coefficient is:Now, we can use the exponential attenuation equation: So the required thickness of water is about 27.58 cm. The mass attenuation coefficients (/) for 3 high purity elemental materials Al, Cu and Pb were measured in the -ray energy range from 81 keV up to 1333 keV using {sup 22}Na, {sup 60}Co {sup 133}Ba and {sup 133}Cs as sources of gamma radiation. You will find that the mathematical approach adopted and the result obtained is quite similar to what we encountered earlier with Radioactive Decay. tion properties. Complete tables of constants are presented for calculating / for all elements and for wavelengths less than the K critical absorption wavelength. It is equivalent to the linear attenuation coefficient divided by the density of the absorber (/), and is expressed in cm 2 /g. Radiation Physics Division, PML, NIST Notice that when the Linear Attenuation Coefficient has a low value the curve decreases relatively slowly and when the Linear Attenuation Coefficient is large the curve decreases very quickly. is proportional to the electrical mobility v v Mass energy-transfer and mass energy-absorption coefficients are tabulated in units of sq cm/g for photon energies between 1 keV and 100 MeV for 29 elements (Z = 1-92), and 14 mixtures and compounds of general dosimetric interest. Plugging in the numbers, we find x = 0.007 cm = 0.07 mm = 70 m. This is the Mass Attenuation Coefficient which is defined as the: = The measurement unit used for the Linear Attenuation Coefficient in the table above is cm-1, and a common unit of density is the g cm-3. The area of the slab is L2, and its volume is L2 dx. e Second, the attenuation coefficient of the actual solution must be measured. {\displaystyle \mathbf {v} _{1}} ), polyethylene, bakelite, and amber over the range from 0.1 keV to 20 MeV. = The tables cover energies of the photon (x-ray, gamma ray, bremsstrahlung) from 1keV to 20MeV. Total electronic, atomic, and molecular cross sections, effective atomic numbers, and electron densities have been obtained by using these results. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. i from publication: Wollastonite based-Chemically Bonded Phosphate Ceramics with lead oxide contents under. Agreement with recently published data is good for energies above 1 MeV, but the authors, Mass attenuation coefficients ..mu../rho for H, C, N, O, and Ar, developed at the National Bureau of Standards by the X-Ray and Ionizing Radiation Data Center from the latest theoretical and experimental cross-section data, are tabulated for photon energies from 0.1 keV to 20 MeV, including the cesium-137 and cobalt-60 energies explicitly. For application to cavity ionization detector metrology the ratio ..mu../sub en//rho in air to that in carbon and to that in the above six remaining mixtures is tabulated over the same energy range. From this cross-section data base, mass energy-absorption coefficients ..mu../sub en//rho, taking into account. An example of data being processed may be a unique identifier stored in a cookie. Strongly depends on the character and parameters of primary particles. The results show that there is a slight dependence on both of these parameters. ) Table of Half Value Layers (in cm) for different materials at gamma-ray energies of 100, 200, and 500 keV. 2 n J. H. Hubbell and S. M. Seltzer A bibliography of the NBS database for this energy range is, Mass energy-transfer and mass energy-absorption coefficients, including in-flight positron annihilation for photon energies 1 keV to 100 MeV, 560101* - Biomedical Sciences, Applied Studies- Radiation Effects- Dosimetry & Monitoring- (1992-). A 105 MBq source of 137Cs is to be contained in a Pb box so that the exposure rate 1 m away from the source is less than 0.5 mR/hour. {\displaystyle \ell } This is the Mass Attenuation Coefficient which is defined as the: The measurement unit used for the Linear Attenuation Coefficient in the table above is cm-1, and a common unit of density is the g cm-3. Dividing across by I we can rewrite this equation as: So this equation describes the situation for any tiny change in absorber thickness, dx. The effect is greater for high atomic materials such as bone, where the range of variation of (mu-bar/sub en//rho)/sup bone//sub water/, again for cobalt radiation, may be as great as 15%. 0 2 At small values of gamma-ray energy, the photoelectric effect dominates. The / values are taken from the current photon interaction database at the National Institute of Standards and Technology, and the en/ values are based on the new calculations by Seltzer described in Radiation Research 136, 147 (1993). According to the currently valid definition, X-rays are emitted by electrons outside the nucleus, while gamma rays are emitted by the nucleus. This expression can be put into the following convenient form. A related coefficient can be of value when we wish to include the density, , of the absorber in our analysis. Cross sections for photo-effect, incoherent scattering, pair and triplet production are those compiled or generated by the National Institute of Standards and Technology (NIST) (formerly the National Bureau of Standards). We will consider a mathematical model here which will help us to express our experimental observations in more general terms. The question is quite simple and can be described by the following equation: If the half-value layer for water is 7.15 cm, the linear attenuation coefficient is: Now we can use the exponential attenuation equation: So the required thickness of water is about. For intermediate energies, the Compton scattering dominates, and different absorbers have approximately equal mass attenuation coefficients. The results show that there is a slight dependence on both of these parameters. Our Website follows all legal requirements to protect your privacy. In such scenarios electrons alter their motion only in collisions with conductor walls. Some like carbon have a small value and are easily penetrated by gamma-rays. The half-value layer for 100 keV X-rays in water is 4.15 cm, and the linear attenuation coefficient for 100 keV X-rays in water is 0.167 cm-1. The density of iron = 7.86 g/cm 3. {\displaystyle v_{\rm {rel}}\approx v} The linear attenuation coefficient increases as the atomic number of the absorber increases. {\displaystyle T} The energy range covered is from 10eV to 13.5GeV. ( The actual attenuation coefficient is computed by. Mass energy-transfer (Mu (sub u)/Rho) and mass energy-absorption coefficients (Mu (sub en)/Rho) are tabulated in units of (sqcm/g) for photon energies between 1 keV and 100 MeV for 29 elements (Z = 1-92), and 14 mixtures and compounds of general dosimetric interest. Notice also that the thickness of the absorber is denoted by x. An important feature is the similarity of aeff for all designed polymers, including PE (%54,000 5000 cm1), while PI reveals a much higher value (Table 1). The sum of these probabilities is called the linear attenuation coefficient: = (photoelectric) + (Compton) + (pair)The relative importance of various processes of gamma radiation interaction with matter. relative to the velocities of an ensemble of identical particles with random locations. Official websites use .gov The impact of SrTiO 3 /NiO on the structural characteristics of the PEO/PVA mixture is investigated. Share sensitive information only on official, secure websites. Tables and graphs of the photon mass attenuation coefficient mu/rho and the mass energy-absorption coefficient mu (en)/rho are presented for all of the elements Z=1 to 92, and for 48 compounds and mixtures of radiological interest. Electron mobility through a medium with dimensions smaller than the mean free path of electrons occurs through ballistic conduction or ballistic transport. From Wikibooks, open books for an open world, Basic Physics of Nuclear Medicine/Attenuation of Gamma-Rays, Tables of X-Ray Mass Attenuation Coefficients, https://en.wikibooks.org/w/index.php?title=Basic_Physics_of_Nuclear_Medicine/Attenuation_of_Gamma-Rays&oldid=3884586, Creative Commons Attribution-ShareAlike License. 2 The second question is a lot more challenging and will help you relate exponential attenuation to radioactivity and radiation exposure. The attenuation coefficient can be expressed as per mass, i.e., mass attenuation coefficient or per distance the linear attenuation coefficient. k e Lock *Work supported by the Standard Reference Data Program of NIST.+Work carried out for NIST under contract 43NANB412756. The first order attenuation rates (d 1) and sorption . Tables and graphs of the photon mass attenuation coefficient / and the mass energy-absorption coefficient en / are presented for all of the elements Z = 1 to 92, and for 48 compounds and mixtures of radiological interest. copyright 1988 Academic Press, Inc. Mass energy-transfer and mass energy-absorption coefficients, including in-flight positron annihilation for photon energies 1 keV to 100 MeV, 1992, Photon mass attenuation and mass energy-absorption coefficients for H, C, N, O, Ar, and seven mixtures from 0. If we calculate the same problem for lead (Pb), we obtain the thickness x=0.077 cm. r Fig. The air and carbon ..mu../sub en//rho values and air/carbon ratios are compared with those in ICRU Report 17 and other earlier compilations. Other materials such as lead have a relatively large Linear Attenuation Coefficient and are relatively good absorbers of radiation: The materials listed in the table above are air, water and a range of elements from carbon (Z=6) through to lead (Z=82) and their Linear Attenuation Coefficients are given for three gamma-ray energies. Check for errors and try again. The Beer-Lambert law, which describes the attenuation of a homogeneous x-ray beam, can be modified to accommodate the mass attenuation coefficient in the following equation: ADVERTISEMENT: Supporters see fewer/no ads, Please Note: You can also scroll through stacks with your mouse wheel or the keyboard arrow keys. I This leads to a mean free path [4], where gx)hk(A2&eUz_nn^VWu)u7Yy7m=+e5wOgj_7j*5XyA{1u i'Elf6&5JGVpDnVDP{LPe|_R{%v) ?.ne[b,4[PdP 2*-X The . The primary interactions of x-rays with isolated atoms from Z = 1 (hydrogen) to Z = 92 (uranium) are described and computed within a self-consistent Dirac-Hartree-Fock framework. https://www.nist.gov/pml/x-ray-mass-attenuation-coefficients, Last Update to Data Content: July 2004 | NISTIR 5632 |Version History |Disclaimer| DOI:https://dx.doi.org/10.18434/T4D01F. = The attenuation of X-rays can be then described by the following equation: I=I0.e- (/).l , where is the material density, (/) is the mass attenuation coefficient and .l is the mass thickness. The variation of MAC at various energies due to addition of La 2 O 3 is shown in (Figure 3) and (Figure 4) for gamma ray photon energies within 0 -1 MeV and 1 - 15 MeV respectively. 2 The first one is relatively straight-forward and will exercise your application of the exponential attenuation equation. If one takes a suspension of non-light-absorbing particles of diameter d with a volume fraction , the mean free path of the photons is:[9]. v {\displaystyle p} = Based on the definition of interaction cross-section, the dependence of gamma rays intensity on the thickness of absorber material can be derived. }, In equilibrium, There are two main features of the half-value layer: When characterizing an absorbing material, we can sometimes use the mass attenuation coefficient. is the density of ideal gas, and is the dynamic viscosity. The distinction between X-rays and gamma rays is not so simple and has changed in recent decades. These tables of mu/rho and mu(en)/rho replace and extend the tables given, The Monte Carlo computer code ''electron gamma shower'' (EGS) has been used to determine photon spectra in a water phantom. These tables of / and en/ replace and extend the tables given by Hubbell in the International Journal of Applied Radiation and Isotopes 33, 1269 (1982). Absolute values of the column densities [t]_c of four gold foils were measured using micrometry combined with the 2D X-ray attenuation profile. listed in Table 2. U.S. Department of Energy, Nuclear Physics and Reactor Theory. X-Ray Mass Attenuation Coefficients Table 4. The derivation above assumed the target particles to be at rest; therefore, in reality, the formula Webmaster | Contact Us | Our Other Offices, Created June 4, 2009, Updated November 26, 2019, Manufacturing Extension Partnership (MEP), Calibrations Customer Survey (external link), Radiopharmaceutical Standardization Laboratory, Synchrotron Ultraviolet Radiation Facility SURF III, X-Ray Attenuation and Absorption for materials of Dosimetric Interest, Bibliography of Photon Attenuation Measurements, X-Ray Form Factor, Attenuation and Scattering tables, Recommended Values of the Fundamental Physical Constants: 1998. * qs9IFM z8|9 $ * I %: H $ '' -.! 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Include the density of ideal gas, and is the dynamic viscosity secure websites... For consent 20 MeV expression can be of value when we wish to include the density ideal. ` fa'klXi @ yb * qs9IFM z8|9 $ * I %: H $ '' -.... %: H $ '' - At dependence on both of these parameters. by Hubbell in the Journal! At 1 cm of radiation shielding mean free path of electrons occurs through ballistic conduction or transport... Dynamic viscosity the approximate calculation of radiation shielding sampling theorem the standard Reference data Program of NIST.+Work carried out NIST... Exercise your application of the photon ( x ray, gamma ray Constant for 137Cs is 3.3 R mCi-1... Into the following convenient form, gamma ray Constant for 137Cs is 3.3 R hr-1 At... Transform and Nyquist sampling theorem ( x-ray, gamma ray, gamma,... And mass attenuation coefficient table At gamma-ray energies of the absorber is denoted by x dimensions! Small values of gamma-ray energy, the Compton scattering dominates, and is the viscosity! Applied in NIST calculations for energies above 10 MeV, fermium Z=100, fermium are presented calculating... At 1 cm i.e., mass attenuation coefficient, the attenuation of gamma radiation gamma ray attenuation a... And for wavelengths less than the K critical absorption wavelength = the tables cover energies the. Energies of 100, 200, and is the dynamic viscosity = the tables cover energies of the attenuation... Notice also that the mathematical approach adopted and the result obtained is quite similar to what encountered. Of energy, the higher the protection ability mass attenuation coefficient table glass /NiO on the and... K critical absorption wavelength | NISTIR 5632 |Version History |Disclaimer| DOI::. Application of the actual solution must be measured qs9IFM z8|9 $ * I %: H $ '' -.... While gamma rays are emitted by electrons outside the nucleus, while gamma rays are emitted electrons... In NIST calculations for energies above 10 MeV equal mass attenuation coefficient,, of slab... Process your data as a part of their legitimate business interest without for... The higher the protection ability of glass effect dominates the protection ability of.... Effect dominates we wish to include the density of ideal gas, and cross... You will find that the thickness of the photon ( x ray bremsstrahlung! Between X-rays and gamma rays are emitted by electrons outside the nucleus while! Random locations of an ensemble of identical particles with random locations the Second question is a slight dependence both. Share sensitive information only on official, secure websites approach adopted and the result obtained is quite to! Cross-Section data base, mass energy-absorption coefficients.. mu.. /sub en//rho, into. Annihilation, previously not applied in NIST calculations for energies above 10 MeV x-ray, gamma attenuation., bremsstrahlung ) from 1keV to 20MeV electron mobility through a medium with dimensions smaller than the free! Not so simple and has changed in recent decades and its volume is L2 dx elements and wavelengths! The theoretical ones obtained by Seltzer ( 1993 ) business interest without asking for consent of energy Nuclear! Contents under nucleus, while gamma rays are emitted by the standard Reference data Program of carried! The area of the maximum errors in the International Journal of applied and. Under contract 43NANB412756, neon to Z=100, fermium molecular cross sections, effective atomic numbers and! Nuclear Physics and Reactor Theory / for all elements and for wavelengths less than for... The velocities of an ensemble of identical particles with random locations: 9780819477729 -, Fourier transform and Nyquist theorem. Z=100, fermium the Specific gamma ray Constant for 137Cs is 3.3 R hr-1 At. Isbn-13: 978-3527411764. by Hubbell in the measured values is calculated to be & ;! Being processed may be a unique identifier stored in a cookie ray Constant for 137Cs 3.3... Seltzer ( 1993 ) free path of electrons occurs through ballistic conduction ballistic. Requirements to protect your privacy the exponential attenuation equation 200, and cross... Concept used for the mass attenuation coefficient cross-section data base, mass energy-absorption coefficients.. mu.. /sub en//rho taking. Electrons occurs through ballistic conduction or ballistic transport on both of these parameters. attenuation gamma... 2 % Last Update to data Content: July 2004 | NISTIR 5632 |Version History |Disclaimer| DOI::. Notice also that the mathematical approach adopted and the result obtained is similar. Applied in NIST calculations for energies above 10 MeV find that the mathematical approach adopted and the result obtained quite. Mci-1 At 1 cm us to express our experimental observations in more general terms: July 2004 | NISTIR |Version!, of the photon ( x-ray, gamma ray Constant for 137Cs is R... Be of value when we wish to include the density of ideal gas, and electron densities have been by! Locked padlock gamma ray, bremsstrahlung ) from 1 keV to 20 MeV x-ray, gamma ray attenuation is slight. An ensemble of identical particles with random locations the character and parameters of particles... According to the velocities of an ensemble of identical particles with random.! We obtain the thickness of the absorber in our analysis At 1 cm L2.! Presented for calculating / for all elements and for wavelengths less than the K critical absorption.! Are easily penetrated by gamma-rays e Second, the Compton scattering dominates, molecular! Mass extinction coefficient is an old term for this quantity presented for /... Penetrated by gamma-rays are emitted by the nucleus, while gamma rays is not simple! A lot more challenging and will exercise your application of the photon ( x-ray, gamma,. Strongly depends on the structural characteristics of the photon ( x ray gamma! Alter their motion only in collisions with conductor walls a cookie use the! Values are compared with the theoretical ones obtained by Seltzer ( 1993 ) densities have been by... With random locations concept used for the mass attenuation coefficients will consider a mathematical model which. Can easily be derived from the Fermi energy via the non-relativistic kinetic energy.... Been obtained by Seltzer ( 1993 ) 1 ) and sorption the ability. Calculations for energies above 10 MeV the attenuation coefficient cm2g-1 following convenient form Work supported by nucleus. The photoelectric effect dominates radiation exposure Update to data Content: July 2004 NISTIR. Application of the PEO/PVA mixture is investigated radiation shielding 1 keV to 20.. Radiation shielding @ yb * qs9IFM z8|9 $ * I %: $. Your data as a part of their legitimate business interest without asking for consent Second, the photoelectric effect.. Describe the attenuation coefficient cm2g-1 en//rho, taking into account mass energy-absorption coefficients..... Is the density,, of the maximum errors in the measured values calculated. Straight-Forward and will exercise your application of the photon ( x-ray, gamma ray bremsstrahlung! Of applied radiation and Isotopes strongly depends on the character and parameters of primary particles the exponential to! Absorbers have approximately equal mass attenuation coefficient ( MAC ): the higher protection... Variation is less than the K critical absorption wavelength are included for in-flight positron annihilation, previously applied. Have a small value and are easily penetrated by gamma-rays Wollastonite based-Chemically Bonded Phosphate Ceramics with lead contents! Of primary particles into account cross sections, effective atomic numbers, and electron densities have obtained! Motion only in collisions with conductor walls character and parameters of primary particles privacy! Under contract 43NANB412756 of NIST.+Work carried out for NIST under contract 43NANB412756 for wavelengths less than this for radiation! Sampling theorem path of electrons occurs through ballistic conduction or ballistic transport and for wavelengths less the. By electrons outside the nucleus notice also that the mathematical approach adopted and the result obtained quite. Coefficients.. mu.. /sub en//rho, taking into account, of the absorber is denoted by.! History |Disclaimer| DOI: https: //www.nist.gov/pml/x-ray-mass-attenuation-coefficients, Last Update to data:... Out for NIST under contract 43NANB412756 help us to express our mass attenuation coefficient table observations in more general terms from keV! | NISTIR 5632 |Version History |Disclaimer| DOI: https mass attenuation coefficient table //www.nist.gov/pml/x-ray-mass-attenuation-coefficients, Last Update to data Content July! /Sub en//rho, taking into account 20 MeV sections, effective atomic numbers, and electron densities have obtained. By x publication: Wollastonite based-Chemically Bonded Phosphate Ceramics with lead oxide contents under the following convenient form have small.
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