Part III: What tools are used to identify elements?What importance do X-rays have to astronomy?From: X-ray Spectroscopy andthe Chemistry of Supernova RemnantsA Series of Lesson Plans byAllie Hajian and Maggie Masetti (NASA/GSFC, Greenbelt, MD)Rick Fowler (Crossland High School, Temple Hills, Maryland)Angela Page (Hyattsville Elementary School, Hyattsville, Maryland)ObjectivesStudents will read and write about the chemistry and spectroscopy of stars and supernovaremnants, as well as understand their relevance and impact on human life. Students willalso learn about cutting edge technology that will help us to build better instruments withwhich to study the Universe.Each section has several pages of background material relevant to the associatedactivities and the lesson plan as a whole. The background sections include short exercisesor thought questions developed to help the student reach a better understanding of thematerial presented. Each section also has activities developed by real teachers - designedto bring important concepts in astronomy right into the classroom. Each activity iscorrelated to national science and math standards for grades 9 - 12. These activities showhow interrelated chemistry, physics, and astronomy really are.1X-ray Spectroscopy & Chemistry of Supernova RemnantsPart III: What tools are used to identify elements? What importance do X-rays have toastronomy?
Outline of UnitPart I: How and Where are Elements Created? Background: The Life Cycles of Stars: How Supernovae Are Formed – Describesthe life of a high-mass star - as well as its death in a giant supernova explosion. Background: The Dispersion of Elements – Describes how supernova explosionsnot only disperse the elements created inside a star, they create new elements. Activity: Fusion Reactions – In this activity, each student is given a card with anelement produced inside stars on it - the students then form fusion reactions thatoccur within stars.Part II: What is Electromagnetic (EM) Radiation? How is itcreated in atoms? What units are used to characterize EMradiation? Background: How Do the Properties of Light Help Us to Study Supernovae andTheir Remnants? – Students learn about the electromagnetic spectrum. Activity: Calculation Investigation – Students learn about unit analysis byconverting energies to wavelengths to frequencies. Background: Atoms and Light Energy – Describes how atoms emit light, andhow we can use this to learn about astronomical objects. Activity: Calculate the Energy! – Students will calculate the energy differences indifferent energy states of the Bohr atom of Hydrogen.Part III: What tools are used to identify elements? Whatimportance do X-rays have to astronomy? Background: Introduction to Spectroscopy – Everything you ever wanted toknow about spectroscopy but were afraid to ask! Activity: Graphing Spectra – Practice drawing graphs of spectra, andunderstanding the different ways spectra can be represented, as well as what eachrepresentation can tell us. Activity: Flame Test – A chemistry experiment that shows how heated elementsemit different colors of light. Activity: Design an Element Poster Advertisement – Students will discuss whatthey have learned about atoms and elements in their own words, designing aposter advertisement for their chosen element. Students will use more than justtheir right brain to think about science!2X-ray Spectroscopy & Chemistry of Supernova RemnantsPart III: What tools are used to identify elements? What importance do X-rays have toastronomy?
Part IV: How does the newest technology help us to understandthe Universe? Background: All About The Microcalorimeter – All about microcalorimetertechnology, the next generation X-ray spectrometer. Activity: Identifying Light Energy by Temperature Changes – Learn first handhow a microcalorimeter really works Activity: Identifying Elements in Supernova Remnants using Spectra – Now thestudents get to take all they have learned and really apply it. Students will identifythe elements present in a supernova remnant by analyzing its spectrum. Background: A Plethora of X-ray Telescopes – Learn about existing and futureX-ray telescopes and what they hope to accomplish. Activity: Satellite Venn Diagram – Students will organize the information aboutX-ray observatories into a Venn diagram. Activity: Writing Assignment – As a closing activity, students will demonstratethe ability to use text information and data to persuade a reading audience of thebenefits of using calorimeter detectors to do X-ray astronomy.3X-ray Spectroscopy & Chemistry of Supernova RemnantsPart III: What tools are used to identify elements? What importance do X-rays have toastronomy?
Part III: What tools are used to identify elements?What importance do X-rays have to astronomy?Introduction to SpectroscopySpectroscopy is a complex art - but it can be very useful in helping scientistsunderstand how an object like a black hole, neutron star, or active galaxy is producinglight, how fast it is moving, and even what elements it is made of. A spectrum issimply a chart or a graph that shows the intensity of light being emitted over a rangeof energies. Spectra can be produced for any energy of light - from low-energy radiowaves to very high-energy gamma rays.Spectra are complex because each spectrum holds a wide variety of information. Forinstance, there are many different mechanisms by which an object, like a star, canproduce light - or using the technical term for light, electromagnetic radiation. Each ofthese mechanisms has a characteristic spectrum.Let's look at a spectrum and examine each part of it.To the right is an X-ray spectrum madeusing data from the ASCA satellite. It isof a supernova remnant (SNR) - a SNRis a huge cloud of gaseous matter sweptup from the explosion of a massive star.The x-axis shows the range of energy oflight that is being emitted. The y-axis ofthe graph shows the intensity of thelight recorded by the instrument fromthe SNR – that is, the number ofphotons of light the SNR is giving offat each energy, multiplied by the sensitivity of the instrument at that energy. We can tellthat the light, or radiation, from this SNR is very high energy - if we look at the units ofthe x-axis - we can see that the photons of light have energies measured in keV, or kiloelectron Volts. A kilo-electron Volt is 1000 electron Volts (eV). This puts is the X-rayrange of the electromagnetic spectrum.The graph shows a decreasing curve, with lots of bumps in it. The curve itself is called acontinuum – it represents X-ray photons emitted at all energies continuously. The X-raysthat are producing this continuum can be caused by several mechanisms that arecompletely different than those producing the X-rays at the various peaks and bumps onX-ray Spectroscopy andthe Chemistry of Supernova Remnants37
the curve. The peaks and bumps are called line emission. Not only are these two differentkinds of X-ray emission (continuum and line) produced differently, but they each tell usdifferent things about the source that is emitting them.The Electromagnetic SpectrumWhite light (what we call visible or optical light) can be split up into its colors easily andwith a familiar result – the rainbow. All we have to do is use a slit to focus a narrowbeam of the light at a prism. This set-up is actually a basic spectrometer.The resultant rainbow is really a continuous spectrum that shows us the different energieslight (from red to blue) present in visible light. But the electromagnetic spectrumencompasses more than just optical light – it covers all energies of light extending fromlow-energy radio waves, to microwaves, to infrared, to optical light, to ultraviolet, to veryhigh-energy X- and gamma-rays.Line EmissionInstead of using our spectrometer on a light bulb, what if we were to use it to look a tubeof gas – for example, hydrogen? We would first need to heat the hydrogen to very hightemperatures, or give the atoms of hydrogen energy by running an electric currentthrough the tube. This would cause the gas to glow – to emit radiation. If we looked at thespectrum of light given off by the hydrogen gas with our spectroscope, instead of seeing acontinuum of colors, we would just see a few bright lines. Below we see the spectrum,the unique fingerprint of hydrogen.These bright lines are called emission lines. Remember how we heated the hydrogen togive the atoms energy? By doing that, we excited the electrons in the atom - when theelectrons fell back to their ground state, they gave off photons of light at hydrogen'scharacteristic energies. If we altered the amount or abundance of hydrogen gas we have,we could change the intensity of the lines, that is, their brightness, because more photonswould be produced. But we couldn't change their color - no matter how much or howlittle hydrogen gas was present, the pattern of lines would be the same. Hydrogen'spattern of emission lines is unique to it. The brightness of the emission lines can give us agreat deal of information about the abundance of hydrogen present. This is particularlyuseful in a star, where there are many elements mixed together.X-ray Spectroscopy andthe Chemistry of Supernova Remnants38
Each element in the periodic table can appear in gaseous form and will each produce aseries of bright emission lines unique to that element. The spectrum of hydrogen will notlook like the spectrum of helium, or the spectrum of carbon, or of any other element.Hydrogen:Helium:Carbon:We know that the continuum of the electromagnetic spectrum extends from low-energyradio waves, to microwaves, to infrared, to optical light, to ultraviolet, to X and gammarays. In the same way, hydrogen's unique spectrum extends over a range, as do thespectra of the other elements. The above spectra are in the optical range of light. Lineemission can actually occur at any energy of light (i.e. visible, UV, etc.) and with anytype of atom, however, not all atoms have line emission at all wavelengths. Thedifference in energy between levels in the atom is not great enough for the emission to beX-rays in atoms of lighter elements, for example.Different Graphical Representations of SpectraThe sample spectra above represent energy emission as lines, the amount of photons oflight represented by the brightness and width of the line. But we can also make agraphical representation of a spectrum. Instead of the emission of a characteristic energybeing shown as a line, it can be shown as a peak on a graph. In this case, the height andwidth of the peak show its intensity. One example of this is the very first spectrum welooked at – the one of the supernova remnant. The peaks and bumps on the graph aresimply a graphical representation of the emission lines of different elements.Below, you will see the spectrum of the Sun at ultraviolet wavelengths. There are distinctlines (in the top graph) and peaks (in the bottom one) and if you look at the X-axis, youcan see what energies they correspond to. For example, we know that helium emits lightat a wavelength of 304 Ångstroms, so if we see a peak at that wavelength, we know thatthere is helium present.X-ray Spectroscopy andthe Chemistry of Supernova Remnants39
Spectra and AstronomyIn a star, there are actually many elements present. The way we can tell which ones arethere is by looking at the spectra of the star. In fact, the element helium was firstdiscovered in the Sun, before it was ever discovered on Earth. The element is named afterthe Greek name for the Sun, Helios. The science of spectroscopy is quite sophisticated.From spectral lines astronomers can determine not only the element, but also thetemperature and density of that element in the star. Emission lines can also tell us aboutthe magnetic field of the star. The width of the line can tell us how fast the material ismoving, giving us information about stellar wind. If the lines shift back and forth, itmeans that the star may be orbiting another star - the spectrum will give the informationnecessary to estimating the mass and size of the star system and the companion star. Ifthe lines grow and fade in strength we can learn about the physical changes in the star.Spectral information, particularly from energies of light other than optical, can tell usabout material around stars. This material may have been pulled from a companion starby a black hole or a neutron star, where it will form an orbiting disk. Around a compactobject (black hole, neutron star), the material in this accretion disk is heated to the pointthat it gives off X-rays, and the material eventually falls onto the black hole or neutronstar. It is by looking at the spectrum of X-rays being emitted by that object and itssurrounding disk that we can learn about the nature of these objects.X-ray Spectroscopy andthe Chemistry of Supernova Remnants40
Continuum EmissionJust like visible light, with its range of energies from red to blue, X-rays have acontinuum, or a range of energies associated with it. X-rays usually range in energy fromaround 0.5 keV up to around 1000 keV.Like line emission, continuum X-ray emission involves charged particles. Continuumemission is a result of the acceleration of a population of charged particles. All X-raysources contain such particles. These particles must be at least partially ionized - theirelectrons need to be unbound from their nuclei to be free to zip around when they areheated to extreme temperatures. For an electron to radiate X-rays, the gas containing theelectron must have extreme conditions, such as temperatures of millions of degrees,super-strong magnetic fields, or the electrons themselves must be moving at nearly thespeed of light. Extreme conditions can be found in disks of matter orbiting black holes orin supernova remnants. Strong magnetic fields, like those created in the wake of asupernova explosion, can also accelerate fast moving ions in spirals around the field linesto the point of X-ray emission. Electrons can be accelerated to nearly the speed of light inthe shockwave created by a supernova explosion.There are three mechanisms that will produce a continuum X-ray emission. They areSynchrotron Radiation, Bremsstrahlung, and Compton Scattering. The radiationproduced is continuous, and not at the discreet energies of line emission because thepopulations of electrons have a continuous range of energies, and they can be acceleratedthrough a range of energies.Synchrotron radiation is emittedwhen a fast electron interacts with amagnetic field. A magnetic field in anarea an electron is traveling in willcause the electron to change directionby exerting a force on it perpendicularto the direction the electron is moving.As a result, the electron will beaccelerated, causing it to radiateelectromagnetic energy. This is calledmagnetic bremsstrahlung orsynchrotron radiation (after radiationobserved from particle accelerators byImage courtesy of University of Hertfordshirethat name). If the electrons and themagnetic field are energetic enough,the emitted radiation can be in the form of X-rays.X-ray Spectroscopy andthe Chemistry of Supernova Remnants41
Bremsstrahlung occurs when anelectron passes close to a positive ion,and the strong electric forces cause itstrajectory to change. The acceleration ofthe electron in this way causes it toradiate electromagnetic energy – thisradiation is called bremsstrahlung, (fromthe German meaning 'braking radiation').Image courtesy of University of HertfordshireThermal bremsstrahlung occurs in a hotgas, where many electrons are strippedfrom their nuclei, leaving electrons and positive ions. If the gas is hot enough (millions ofKelvin), this kind of radiation will primarily take the form of X-rays.Comptonization is when a photon collideswith an electron – the photon will either giveup energy to or gain energy from the electron,changing the electron's velocity as a result.What Are Some Examples ofContinuum Emission?Gas that is hotter than 10 million degrees, suchImage courtesy of University ofas the gas heated by a supernova explosion,Hertfordshireproduces most of its emission in X-rays fromthermal bremsstrahlung. Gas can be heated tothese temperatures by the outward moving shock of a supernova explosion, or in anaccretion disk around a black hole or neutron star. Synchrotron radiation can produce Xrays around supernova remnants (SNR), where the magnetic fields are strong and ionshave been accelerated by the shock wave to high energies. X-rays produced by SNRrequire electrons with energies of about 104 GeV (Giga electron-Volts) each (you wouldhave to heat an electron to a temperature of about ten trillion degrees for it to have thismuch energy)! Synchrotron radiation and Compton scattered radiation are majorcomponents of the diffuse X-ray background and emission from active galaxies.For the StudentUsing the text, define the following terms: spectroscopy, keV, continuum,continuum emission, line emission, electromagnetic spectrum, synchrotronradiation, bremsstrahlung, comptonization.Reference /science/how sicsInitiative/Physics2000/quantumzone/X-ray Spectroscopy andthe Chemistry of Supernova Remnants42
Activity: Graphing SpectraDays Needed: 1Grade level: 9 - 12ObjectiveStudents will be introduced to two different representations of spectra - the photographicrepresentation, such as the familiar rainbow, and the graphical representation used moreoften by astronomers. Students will explore the differences and similarities of both theserepresentations, and will develop a more intuitive feel for a graphical representation,which may not yet be familiar to them.Science and Math StandardsNCTM Content Standard 8:- Geometry from an Algebraic Perspective Content Standard 10:- StatisticsNSES Content Standard A:- Unifying Concepts and Processes in Science Content Standard C:- Light, Energy and Magnetism- Structure of Atoms and MatterPrerequisites Math Students should understand interpreting and manipulating graphical data. Science Students should understand the concept of a spectrum. Students should have read the Introduction to Spectroscopy.IntroductionA rainbow is often given as an everyday example of a spectrum. Most students have seena rainbow, so this example is used to help make the unfamiliar more familiar. However,the spectra that scientists use, and the spectra that students will see in this lesson plan,appear very different than a rainbow. In this activity, students will explore for themselvestwo different representations of the same spectrum, and will be introduced to advantagesand disadvantages of the different representations.EngagementHand out the “Student Worksheet: Graphing Spectra Part 1.” Have the class get intogroups, if they aren't already, and complete it. The class should be discussing theX-ray Spectroscopy andthe Chemistry of Supernova Remnants43
answers, but each writing their own explanation on their own paper. The paper will becollected at the end of class and used as an assessment. The teacher should judge howmuch time they feel the class will need for this exercise.After the class is done, discuss their answers to the questions posed in the worksheet.ElaborationHand out “Student Worksheet: Graphing Spectra Part 2.” Have each student complete iton his or her own. Go over their answers in class when they have completed them. Theteacher may choose to collect and correct the worksheets before discussing the answers inclass.EvaluationFormative assessment and observation should be evident throughout the lesson. Theworksheet, final questions during closure or a future quiz may serve as summativeassessment.ClosureHave students write for three minutes what they have learned about spectra, how they arerepresented and the usefulness of the different representations.X-ray Spectroscopy andthe Chemistry of Supernova Remnants44
Student Worksheet:Graphing Spectra Part 1Below are two examples of the same emission spectrum. The first example is without any"quantitative" data, while the second shows light energy as a function of wavelength. Thex-axis has the same units (wavelength, in this case, although frequency or energy couldalso be used) in both cases, and it runs from 300 to 350 Ångstroms. In your group,discuss the following questions, then write individual answers on paper.1. As you move along the wavelength axis from 300 Ångstroms to 350 Ångstroms, whatwill happen to the amount of energy emitted by the source? Explain why.2. In the second spectrum, explain why the emission lines are at different heights.3. In order for bottom plot to include more "quantitative" data, what variable should goalong the y-axis?4. How is this variable illustrated in both graphs?5. Describe how the second spectrum would look if it were a function of energy (insteadof wavelength).6. What types of information are gathered from both spectra?Solar UV SpectraX-ray Spectroscopy andthe Chemistry of Supernova Remnants45
KEYSolution: Student Worksheet:Graphing Spectra Part 1Below are the answers to the "Think About" questions.1. As you move along the wavelength axis from 300 Ångstroms to 350 Ångstroms, whatwill happen to the amount of energy emitted by the source? Explain why.The energy decreases. This is because the energy is inversely proportional to thewavelength: E hc/l2. In the second spectrum, explain why the emission lines are at different heights.The varying heights represents the different intensities of the lines. The lines in theleft-most portion of the spectrum are brighter than any of the others.3. In order for bottom plot to include more "quantitative" data, what variable should goalong the y-axis?The y-axis should be labeled as "Intensity".4. How is this variable illustrated in both graphs?In the top image, it is represented by the brightness of the line. In the bottom plot, it isrepresented by the height of the line.5. Describe how the second spectrum would look if it was a function of energy (insteadof wavelength).Keeping the usual sense of values increase from left to right, the order the emissionlines would be flipped left-to-right. That is, the brightest lines would be on the right.6. What types of information are gathered from both spectra?From the spectra, we can identify the emission lines. With knowledge of thecharacteristic emission lines of various elements, we could then identify the elementsgiving rise to this spectrum.Solar UV SpectraX-ray Spectroscopy andthe Chemistry of Supernova Remnants46
Student Worksheet:Graphing Spectra Part 2The following spectrum represents the energy state of the element, carbon. Carbon'semission lines in the visible range are a function of wavelength from 4,000 to 7,000Ångstroms. You are going to create a graphical representation of carbon's spectrum fromthe photographic representation. Refer to the example above to help. At the particularwavelengths, illustrate the varying brightness of carbon's emission lines. Notice that inthe photographic representation of the spectrum there is an underlying continuum ofemission, in addition to the bright spectral lines. This continuum is due to contaminationof the spectrum by ambient light, such as small amounts of white light that are picked upby the spectrometer. Your graphical representation should include this low level ofemission at all wavelengths as well as carbon's spectral line features.X-ray Spectroscopy andthe Chemistry of Supernova Remnants47
Below you are given spectra for both hydrogen and helium. For each element, select twoof the brightest emission lines at the particular wavelengths and measure thewavelengths. The ruler below indicates the scale of the spectrum. Solve for the frequencyand energy of these lines, using the relationships between wavelength and frequency andbetween frequency and energy. (Hint: You will have to manipulate an equation.) Afterthe flame test, you will complete the same calculations for the following elements:sodium and calcium.X-ray Spectroscopy andthe Chemistry of Supernova Remnants48
KEYSolution: Student Worksheet:Graphing Spectra Part 2The graphical representation should include all visible lines shown in the color spectrum.The continuum should rise gradually from 4000 Ångstroms, and remain fairly constantthrough blue, and decrease slightly in green portion of the spectrum. It should increaseagain, reach a maximum near yellow, and then decline again in the red.Below are the solutions for the identifying the lines in the spectra of hydrogen andhelium.HydrogenWe can identify three bright lines for hydrogen in the top spectrum. Measuring from thescale, the wavelengths are 435 nm (purple), 486 nm (blue) and 657 nm (red). Recall (e.g.from the Calculation Investigation) that the frequency is given by ν c/λ, and the energyis given by E hν (where h 6.626 10-34 J-s, and c 3 108 m/s). In the table belowwe summarize the frequency and energy results for these lines. (We include the color toaid in identifying the line in the spectrum.)X-ray Spectroscopy andthe Chemistry of Supernova Remnants49
Wavelength (nm)ColorFrequency (Hz)Energy (J)435purple6.90 10144.57 10-19486blue6.17 10144.09 10-19657red4.57 10143.03 10-19HeliumWe can identify a number of lines in the spectrum of Helium. The bright lines are listedin the table below, along with their frequencies and energies. Students may identify anytwo of these.Wavelength (nm)ColorFrequency (Hz)Energy (J)447purple6.71 10144.45 10-19469blue6.40 10144.24 10-19472blue6.36 10144.21 10-19493blue-green6.09 10144.03 10-19501blue-green5.99 10143.97 10-19505blue-green5.94 10143.94 10-19587yellow5.11 10143.39 10-19669red4.48 10142.97 10-19X-ray Spectroscopy andthe Chemistry of Supernova Remnants50
Activity: Flame TestDays Needed 1.5 DaysGrade level 9 - 12ObjectiveStudents will discover first hand how different elements emit different specificwavelengths of light energy when burned, and that these can be identified when the lightis separated with a prism.Science and Math StandardsNCTM Content Standard 2:- Mathematics as Communication Content Standard 4:- Mathematics as Connections Content Standard 8:- Geometry from an algebraic perspectiveNSES Content Standard B:- Abilities necessary to do scientific inquiry- Understandings about scientific inquiry Content Standard C:- Structure of Atoms- Interactions of energy and matter Content Standard G:- Nature of Scientific Knowledge- Historical PerspectivesPrerequisites Math Students should have had some Pre-Algebra, especially in the areas ofmanipulation of formulas and pattern recognition. Science Students should have had an introduction to the electromagneticspectrum, the concept of a spectrum and how atoms emit light energy.IntroductionRecalling the characteristics of atoms and light, the flame test is a great way to physicallydemonstrate some of the more abstract ideas discussed in the background sections onAtoms and Light Energy and Spectroscopy.X-ray Spectroscopy andthe Chemistry of Supernova Remnants51
ExplorationThe students will work in lab groups of three to four students to construct meaning on thecauses of various light emissions from the following 0.5M chemical solutions: LiCl,NaCl, CuCl, BaCl, CsCl, and CaCl. To prepare for the Flame Test, each 0.5M solutionshould be placed in a test tube by itself. Each of the six test tubes should then be placed atthe various laboratory stations 1 through 6. The students will rotate to each station to testthe solution.Materials 7 test tubestest tube rackplatinum wire or wood splintslaboratory burnergogglesapron0.5M solutions of LiCl, NaCl, CuCl, BaCl, CsCl and CaCl, and 1M of HClHand out “Student Worksheet: Flame Test” student worksheet. Have the students answerthe thought questions at the end of Part I in groups, but on paper. They should be utilizedto facilitate a meaningful discussion on light emission. Afterwards, the students shouldcomplete the questions in Part II individually. They may be assigned for homework ifthere is not enough class time.EvaluationFormative assessment and observation should be evident throughout the lesson. Theworksheet, final questions during closure or a future quiz may serve as summativeassessment.ClosureHave students take three minutes to write in their own words why different elementsproduce flames of different colors when burned. How is this quality useful in astronomy?Reference URLFlame s/flametests.htmX-ray Spectroscopy andthe Chemistry of Supernova Remnants52
Student Worksheet:Flame TestPart IProcedure1. Put on lab apron and safety goggles.2. Add 15 drops of each 0.5M solution to a different clean test tube.3. To clean the wire, dip it into the test tube of 1M of HCl and heat the wire in thehottest part of the flame until no color shows.4. When the platinum wire is clean, dip the wire in the test tube containing a 0.5Msolution and hold it in the hottest part of the flame. Record your observation of thecolor of the flame on the data table.5. Repeat the process of cleaning the platinum wire. Now get ready to test anothersolution.6. Test all of the solutions and make sure that you record the color of the flame for eachelement on the Data Table.7. Check your flame colors to known results.8. Fill one clean test tube with 15 drops of one of the 0.5M solutions. The teacher keepstrack of what element solution is in this "mystery tube." Repeat the flame test,without telling the students what solution it is. Students must use the informationgained from the first part of the experiment to identify the mystery solution.9. Use the diffraction grating to observe the color of the flame for the followingelements: Sodium, Barium, Copper, and Lithium. The students should be able to seethe individual lines
Activity: Design an Element Poster Advertisement – Students will discuss what they have learned about atoms and elements in their own words, designing a poster advertisement for their chosen element. Students will use
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021 BIBLIOGRAFI 1. Rujukan Buku Bahasa Arab Abd al-‘AzÊz, AmÊr (1999), Fiqh al-KitÉb wa al-Sunnah: DirÉsah MustafÉdah TatanÉwulu AbwÉb al-Fiqh ‘alÉ Mukhtalif al-MadhÉhib wa al-‘ArÉ wa Tu’raÌu li Ammah al-QadÊyah fÊ Öaw’i al-IslÉm bi UslËbin MauÌË’iyyin Mu’ÉÎirin. j. 5,
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Abattage des roches b. Foration c. Tir d. Chargement et transport CHAPITRE III CALCUL DE LA STABILITE DES TALUS DE LA CARRIERE DE AIN EL KEBIRA III .1. INTRODUCTION III .2. DETERMINATION DES PROPRIETES MECANIQUES DES ROCHES III.2.1. Résistance a la compression III.2.2. Résistance a la traction III.2.3. Cohésion et angle de frottement interne d’un échantillon III.2.4. Fissuration des .
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Index of Resolutions from 1998 Section III.4 - Eames Commission Section III.5 - The Authority of Holy Scriptures Section III.6 - Instruments of the Anglican Communion Section III.7 - The Lambeth Conference Section III.8 - The Virginia Report Section III.9 - Inter-regional groupings Section III.10 - Ma
III-3. Determination of Wire Condition 42 III-4. Wire Recovery Length 42 III-5. Broken Wires 43 III-5.1 Exterior Broken Wires 43 III-5.2 Interior Broken Wires 43 III-6. Cracked Wires 46 III-7. Strength Evaluation using the BTC Method 46 iv
Interactions 1 READING Listening &SPEAKING WEEK 4 Date Unit Part 2 Part 2 Part2 Part 3 Part 3 Part 4 Part 4 Part 4 Interactions 1 READING Listening &SPEAKING WEEK 5 Date Unit Quiz 1 Quiz 1 Chapter 3-Intro-Part 1:P.42-45 Chapter 4- Intro. Part 1 Before You Listen Part 1 :P.46-48 Part 2 Part 1 : After You Listen Part 2
Part No : SVI-II-4X-IP-66 Part No : J023995455177 Part No : CAGE (INNER) 15 Part No : CAGE (OUTER 26 Part No : CAGE GASKET 26 Part No : 010272032-779-0000 Part No : 010275042-24250000 Part No : 008387003-686-0000 Part No : 035107-040-716 Part No : SVI II AP 2112312130 Part No : 35-35212 Part No : 204500389-900-0000 Part No : 021000412-153G0000
Social Science Our Pasts Part-III (Book-1) Our Pasts Part-III (Book-2) Social & Political Life Part-III Resources and Development Geography NCERT Computer Cyber Beans – VIII KIPS Sanskrit Ruchira Part-III NCERT French Apprenons le Francais – Part-IV New Saraswati House Map Book Evergreen .
Practical Scientific Procedures and techniques Internal 3 1 . TBC. . Part 4. Unit 14. Part 1 Part 2 Part 3 Part 4 . Unit 17. Part 1 Part 2 Part 3 Part 4 . Unit 21. Par. t1 . Part 2 Part 3 Part 4 . 5 P a g e . How to Hand In Work . Format of your work Font: Calibri (body) .