Once again, the team appealed to a presentation of PowerPoint to divulge this work. Download available below (Portuguese version only):
Remember that if you have any doubt, the coment zone is open for questions.
Wednesday, 20 January 2010
Planck's Constant - an Experimental Determination Appealing to the Relation of Duane-Hunt
In this publication, the team appealed to a presentation in PowerPoint for the spreading of the work, to have access to this presentation, you can download it in this button (only avaiable in portuguese language):
Remember that if you have any doubt, the coment zone is open for questions..
Moseley's - an Experimental Verification Using X-Ray Fluorescence
This work had for goals to verify experimentally the Moseley's law, that relates the frequencies of the spectral scratches α and β of the series K and L of the characteristic X-rays of some elements and the atomic number, Z, of these elements [2], and to identify qualitatively material using techniques of fluorescence of the X-rays[1].
The experimental system uses an X-ray tube with a 30 keV polarized copper anode as a source for the elements with energy superior to the energi of aluminum, Al, (Kα=1,49keV) and with energy equal or lower than the energy of Indium, In, (Kβ=24,21KeV), for elements with energy superior to Indium it's only possible to indetify Lα. In this work, we analyzed samples of the elements Al, Cl, Ca, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ge, Pd and Pb. For moreover, and with intention to identify to the composition of some objects an liquids, we analyzed a shell, a blade of a penknife, a wooden cup, a rock, a bag with unknown content, a card, several types of gasoline, car oil and a used car oil mixture gasoline.
The characteristic X-Rays, produced per item of the elements, are detected by a Si detector and its energies acquitted in a analytical multicanal[1].
With the objects and used samples of liquid one expects to get a composed specter for some peaks of energy that allow to distinguish and identify each one of the constituent.
Keywords: Moseley's law, X-rays, X-ray fluorescence..
___________________________________________________________
1. Introduction
___________________________________________________________
1. Introduction
A spectral series is a set of lines present in the specter of emission atoms, of one determined element. Each one of these lines is identified with a level of particular energy of an atom of the element in study[3].
In 1895, W. C. Roentgen discovered the X-Rays, sixteen years later C. G. Barkla noticed evidences of series of lines of called emission K, L, M, N, … and in 1913 Moseley showed the existance of the relation between wave length of spectral lines and the atomic number of the element, in this way noticed that copper lines were stronger than Zinc lines in the brass, establishing the base for the qualitative and quantitative analysis using X-rays. Still in the same year, Coolidge, introduced the pipe of X-Rays of high vacuum and M. Sigbahn started to make measurements of wave of the specter of X-Raus of four chemical elements[4].
The Moseley's law can be express as
ν=Q(Z-σ)² (1)
or as
λ^½ =C(Z-σ)(2)
where Q and C are constant of proportionality and σ is the constant call of shield [1]. The law of Moseley can be express as
where Q and C are constant of proportionality and σ is the constant call of shield [1]. The law of Moseley can be express as
where Q and C are constant of proportionality and σ is the constat called of shield[1].
This constant takes a value close to 1 for the one for the spectral series Kα, turning aside itself only for elements bellow Aluminum, Al[1].
This constant takes a value close to 1 for the one for the spectral series Kα, turning aside itself only for elements bellow Aluminum, Al[1].
Although Moseley had empirically derived its formula from the experimental data that square root of the frequencies of X-Raus got through the representation of the atomic number in function, then was possible to explain these results to the light of the atomic model of Bohr. Thus, one concluded that the responsible electron for more intense spectral line (Kα) resulted of the transition of an electron between layers K and L (since a layer next to the moved away nucleus for one more) with n=1 e n=2. The formula of bohr for the Kα transistions would be given by:
(3)The method used in this work, for verification of the Moseley's law, "that it determines that the energy of the characteristic X-Rays for each orbital one is proportional to the square of the atomic number og each element" [1], consists in using a pipe of X-Rays, to excite samples of some elements, and a discriminating multicanal, to measure the energies of characteristic X-Rays emitted for the different elements[1].
The X-Rays are electromagnetic radiation consisting by fotons of raised energy[2]. These possess to be able ionizing, high to be able of penetration and are invisible to the human eye.
In the production of X-Rays, the colision of the beam of electrons with the anode, it produces two types of specters of X-Rays: a continuous specterm that result of the deceleration fo the electron during the penetration in the sample, and other, discrete, called characteristic X-Ray of the anode. The specter of X-Rays results then of the overlapping of a continuous specter anda a series of characteristic spectral lines of the anode[5].
Characteristic X-Rays are after produced the emission of a electron of a more internal layer of atom a radiated with ionizing radiation and consequent transistion of electron of the orbital ones of the atom of higher states for lower states of energy. The energies of thus emitted X-Rays depend on the possivle transistions between orbital and have specific and only values for each element of periodic table. The sctronger characteristic emissions are the correspondentes to the transistions of electrons of the atom for the layer most internal, that is K (Kα e Kβ)[1].
Historically, this experimental work was of the biggest importance to understand and to allow a satisfactory organization of the periodic table, establishing the atomic number of an element as an experimentally measurable amount. This was expressed the capacity to command the elements in the periodic table in accordance with the atomic number instead of the atomic mass, thus exceeding some conceptual problems that had appeared with the previous ordinance, as was the case of the inversion of order of nickel (Z=28, 58,7 u.) and of cobalto (Z=27, 58,9 u.). Thus, the half-quantum model of Bohr/Rutherford became possible to make quantitative forecasts of the spectral lines in accordance with. The fact of the model of Bohr to be able to be used to calculate the spectral lines of ray-x between aluminum (Z=13) and the gold (Z=79) and of this value if to relate with the atomic number helped to corroborate the atomic model of Bohr. Later with the advent of the quantum mechanics, the law of Moseley appeared of course from the theoretical formularizations, by what] was incorporated in the quantum model of the structure of the atom [6.
Historically, this experimental work was of the biggest importance to understand and to allow a satisfactory organization of the periodic table, establishing the atomic number of an element as an experimentally measurable amount. This was expressed the capacity to command the elements in the periodic table in accordance with the atomic number instead of the atomic mass, thus exceeding some conceptual problems that had appeared with the previous ordinance, as was the case of the inversion of order of nickel (Z=28, 58,7 u.) and of cobalto (Z=27, 58,9 u.). Thus, the half-quantum model of Bohr/Rutherford became possible to make quantitative forecasts of the spectral lines in accordance with. The fact of the model of Bohr to be able to be used to calculate the spectral lines of ray-x between aluminum (Z=13) and the gold (Z=79) and of this value if to relate with the atomic number helped to corroborate the atomic model of Bohr. Later with the advent of the quantum mechanics, the law of Moseley appeared of course from the theoretical formularizations, by what] was incorporated in the quantum model of the structure of the atom [6.
Historically, this experimental work was of the biggest importance to understand and to allow a satisfactory organization of the periodic table, establishing the atomic number of an element as an experimentally measurable amount. This was expressed the capacity to command the elements in the periodic table in accordance with the atomic number instear of atomic mass, thus exceeding some conceptual problems that had appeared with the precious ordinance, as was the case of the inversion of order of nickel (Z=28, 58.7 u.) and of cobalt (Z=27, 58.9 u.). Thus, the semi-quantum model of Bohr/Rutherford became possible to make quantitative forecasts of the spectral lines in acoordance with. The fact of the model of Bohr to be able to be used to calculate the spectral lines of X-Ray between aluminum (Z=13 and the gold (Z=79) and of this value if to relate with the atomic number helped to corroborate the atomic model of Bohr. Later with the advent of the quantum mechanics, the Moseley's law appeared of course from the theoretical formularizations, by what was incorporated in quantum model of the structure of the atom[6].
1. Method
1. Method
To obtain information of the energy of the chatacteristic X-Rays of an element is necessary to excite the way element to produce X-Rays. For this it is used a copper X-Ray anode polarized up to 30 keV, wich makes the X-Rays to happen in the element. After this, the X-Rays produced by the element are identified by the detector[1].
The collected information from the detector is sent for an analytical multi-canal that separates the energies of the radiation allowing to create, with the aid of the computer, a specter of energies. This specter is represented by a xy plot where the x axle represents the value of the energy identified and the y axle represents the counting of the number of times that that energy was detected[1].
The more time the process lasts, the more clearly will be the plot in the end of the same process. It is expected that we can observe three aspects in the graph: first, the Bremsstrahlung continuous, secondly, the peaks Kα e Kβ of copper (since that the pipe is made of coppe), and the elements Kα e Kβ peaks (in the case of the element not to have Kα and Kβ but Lα and Lβ, we only can see Lα since that Lβ is unlikely to see in the used resolution.
As the amplitude of the impulses is proportional to the canal number, N, in the analytical multi-canal, we have:
EKα ∝ A ∝ N (4)
Using this relation with Eq.1:
N ∝ Q(Z-σ)
and
N ∝ D(Z-σ) (5)
and
N ∝ D(Z-σ) (5)
where D is a proportionality constant[1].
3. Experimental system
It stops beyond the elements considered in Table I, still will be analyzed objectos and liquid such as a shell, a blade of a penknife, a wooden cup, a rock, a card, non leaded gasoline 95, gasóleo, oil of new car, used oil mixture of car with gasolinas and gasóleo. For the detention of rays X of fluorescence of the some targets of elements [1 is used a detector of radiation of Itself].
Closed Tel-X-ometer
X-ray tube turned on
6. Analysis and Quarrel of the Experimental Results To each one of the graphs gotten with I ADJUST are adjusted it some gaussianas of form to take off the average value of each one of them, that it will correspond to the canal where the peak is found. The following image presents an analyzed typical graph in ADJUSTS it, in this case the corresponding graph to the element has covered.
To obtain to establish a relation between the measured canal and the energy of the detected radiation, recta of adjustment through the method of minimum quadratic shunting lines applied to the values of the canals of the graphs of copper and calcium was carried through one and the respective energies of the Kα and Kβ. Thus recta was gotten following:
Interacção Núcleo-Electrão
3. Experimental system
For the accomplishment of this experience is used the pipe of X-Rays with copper anode as source for the samples[1].
It stops beyond the elements considered in Table I, still will be analyzed objectos and liquid such as a shell, a blade of a penknife, a wooden cup, a rock, a card, non leaded gasoline 95, gasóleo, oil of new car, used oil mixture of car with gasolinas and gasóleo. For the detention of rays X of fluorescence of the some targets of elements [1 is used a detector of radiation of Itself].
It will be analyzed also objects and liquids such as a shell, a blade of a penknife, a wooden cup, a rock, a card and diferent types of gasoline and oil mixtures.
For the detection of X-Rays of fluorescence of the targets of elements it is used a Si radiation detector[1].
For the detection of X-Rays of fluorescence of the targets of elements it is used a Si radiation detector[1].
- Experimental procedure
1) To verify that the tension of the X-Ray pipe from the Tel-X-ometer is in the position of 20 keV;
2) To place the sample in the support for the effect;
Open Tel-X-ometer
Open Tel-X-ometer3) To verify that the line that joins the collimator of the X-Ray pip to the target it finds the same base that the line that crosses the axle of the detector and intercepts the target;
4) To verify that the angle that the target makes with the pipe of X-Rays is approximately equal to what makes with the window of the detector;
5)To close the protection cover;
Closed Tel-X-ometer6) Turn on the oscilloscope;
7) Press the RED button (X-RAYS ON) on the Tel-X-ometer to turn on the X-Ray tube;
X-ray tube turned on6. Analysis and Quarrel of the Experimental Results
To each one of the graphs gotten with AJUSTO are ajusted it some gaussians of form to take off the average value of each one of them, that will correspond to the canal where the peak is found. The following image presents an analyzed typical graph in AJUSTO, in this case the corresponding graph is from the element copper.
To obtain to establish a relation between the measured canal and the energy of the detected radiation, recta of adjustment through the method of minimum quadratic shunting lines applied to the values of the canals of the graphs of copper and calcium was carried through one and the respective energies of the Kα and Kβ. Thus recta was gotten following:
To establish a relation between the measured canal and the energy of the detected radiation, the ajustment function obtained through the method of minimum quadratic shunting lines applied to the vaules of the canals of the graphs of copper and calcium was carried through one and the respective energies of the Kα e Kβ. Here is the obtained linear function:
It was obtained the following Kα e Kβ values for the several elements:
From this results, we can create a plot of the elementar atomic number in order to the square root of the characteristic function of Kα e Kβ.
The element copper is present in all the graphs since the filament (anode) is made of copper.
In all graphs it is possible to observe a continuous specter that does not correspond to no characteristic energy of the element of the sample but of the Bremsstrahlung radiation, existing due to loss of energy from the electron while, in its passage between the source and the sample, it is decelerated and reacelerated resulting interactions with the nuclei of atoms present in the air.
In all graphs it is possible to observe a continuous specter that does not correspond to no characteristic energy of the element of the sample but of the Bremsstrahlung radiation, existing due to loss of energy from the electron while, in its passage between the source and the sample, it is decelerated and reacelerated resulting interactions with the nuclei of atoms present in the air.
Interacção Núcleo-Electrão Following, the several samples and objects with the goal to identift the components:
In all the samples were detected the copper presence, what it is not expressed the copper presence obligatorily in the sample, but yes to the described precess related with the composition of the filament of the light bulb.
From the data of table 3 it is possible to verify that the elements detected in little differ from sample for sample. Such must it the fact of these composites be of organic origin e, for consequência, to correspond to an energy below of that the experimental assembly allows to detect, cannot observe the peaks of carbon. Thus, the specters gotten only in allow them to analyze the presence of elements that if had found in the sample in sufficiently low or even though residual amounts (as it will be the case, for example, of árgon).
From the data of table 3 it is possible to verify that the elements detected in little differ from sample to sample. Such must it the fact of these composites be of organic origin and, for consequence, to correspond to an energy below of that the experimental assembly allows to detect, cannot observe the peaks of carbon. Thus, the specters gotten only in allow them to analyze the presence of elements that if had found in the sample in sufficiently low or even though residual amounts (as it will be the case, for example, of árgon).
Relatively to the analyzed and presented objectos remains in table 4, it was obtained, of satisfactory form, to identify the unknown salt, to the composed departure maioritariamente for chlorine. In relation to the wood, it was verified again that the detected elements are elements that enter in its composition in residual amounts, since the element most abundant - carbon - cannot be detected. It was obtained, of acceptable form, to identify the blade of the penknife as being constituted of a metallic league. To notice that the presence of Kripton in the blade if in accordance with finds the constitution of the new leagues used for the production of this type of tools. In the plate of that if it had the knowledge of that the germanium and another metal were gifts, the iron was identified.
Relatively to the analyzed and presented objects that remain in table 4, it was obtained, of satisfactory form, to identify the unknown salt, to the composed departure of chlorine. In relation to the wood, it was verified again that the detected elements are elements that enter in its composition in residual amounts, since the element most abundant - carbon cannot be detected. It was obtained, of acceptable form, to identify the blade of penknife as being constituted of metalic league. To notice that the presence of Kripton in the blade if in accordance with th findings of the constitution of the new leagues used for the production og this type of tools. In the plate of that if it had the knowledge of that the germanium and another metal were present, the iron was identified.Relatively to the analyzed and presented objectos remains in table 4, it was obtained, of satisfactory form, to identify the unknown salt, to the composed departure maioritariamente for chlorine. In relation to the wood, it was verified again that the detected elements are elements that enter in its composition in residual amounts, since the element most abundant - carbon - cannot be detected. It was obtained, of acceptable form, to identify the blade of the penknife as being constituted of a metallic league. To notice that the presence of Kripton in the blade if in accordance with finds the constitution of the new leagues used for the production of this type of tools. In the plate of that if it had the knowledge of that the germanium and another metal were gifts, the iron was identified.
7. Conclusions
The results are sufficiently precise and exact and, even so the experimental assembly has disclosed the presence of some noise, this was eliminated, successfully, allowing that the measurement was made during more time having gotten an intensity of bigger signal, increased the difference og signal between the noise and the peaks of emission.
On the basis of this experimental assembly, was possible to verify the law of Moseley experimentally. In what it says respect to the identification of the constituent elements of the samples in analysis in this work, can conclude that the analysis is not only possible as it is sufficiently fiável when they intend to inside identify samples constituted of elements of the gamma of operation of the used assembly, but that it becomes difficult or even though impossible when the samples are of organic origin, since, it stops beyond the only detected elements being those that represent a residual percentage of the constitution of the sample, the resultant peaks of the emission of the filament of has covered have an intensity greater very that the remains, thus making it difficult the analysis. Of form to prevent or to exceed this impasse, it would be necessary to use another type of experimental assembly whose gamma of detention could enclose the energies of elements with lesser energies.
On the basis of this experimental assembly, was possible to verify the law of Moseley experimentally. In what it says respect to the identification of the constituent elements of the samples in analysis in this work, can conclude that the analysis is not only possible as it is sufficiently fiável when they intend to inside identify samples constituted of elements of the gamma of operation of the used assembly, but that it becomes difficult or even though impossible when the samples are of organic origin, since, it stops beyond the only detected elements being those that represent a residual percentage of the constitution of the sample, the resultant peaks of the emission of the filament of has covered have an intensity greater very that the remains, thus making it difficult the analysis. Of form to prevent or to exceed this impasse, it would be necessary to use another type of experimental assembly whose gamma of detention could enclose the energies of elements with lesser energies.
On the basis of this experimental assembly, it was possible to verify the Moseley's law experimentally. In what it says respect to the identification of the constituent elements of the samples in analysis in this work, can conclude that the analysis is not only possible as it is sufficiently viable when is intent to identify samples constituted of elements of the gamma of operation of the used assembly, but that it becomes difficult or even impossible when the samples are organic. Of form to prevent or to exceed this impasse, it would be necessary to use another type of experimental assembly whose gamma of detention could enclose the energies of elements with lesser energies.
Bibliographical References:
[1] Oficina de Investigação e Comunicação. Trabalho Nº 1 – “Lei de Moseley – uma Verificação Experimental Utilizando Fluorescência de Raios X “. Departamento de Física da Universidade de Aveiro. (2007/2008)
[2] Portugal, Paulo S. Carriço. Páginas de Professores. Raios X. Lei de Moseley. Visualizado a 8 de Outubro de 2009.
[3] Institute of Electrical and Electronics Engineers (IEEE):
Dictionary.com, "spectral series," in Dictionary.com Unabridged. Source location: Random House, Inc. http://dictionary.reference.com/browse/spectral series.
Available: http://dictionary.reference.com. Accessed: October 11, 20
[4] Tash, Peter; Damiani, Furio; Oliveira, Luiz Cláudio Marangoni. Técnicas de Análise e Caracterização de materiais. X-Rays Fluorescence Spectroscopy. Visualizado a 11 de Outubro de 2000 http://www.dsif.fee.unicamp.br/~Furio/IE607A/XRF.pdf
[5] Vasconcelos, César A. Zen. Apontamentos da disciplina: Física do Século XX B. Departamento de Física da Universidade Federal do Rio Grande do Sul. Visualizado a 11 de Outubro de 2009.
[6] Wikipédia. Tabela Periódia. Visualizado a 23 de Outubro de 2009.
[7] Universidae de Waterloo. Production of X-Rays.
Vizualizado a 11 de Outubro de 2009
Remember that if you have any doubt, the coment zone is open for questions.
Subscribe to:
Posts (Atom)
