Atomic and nuclear physics

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1 Atomic ad uclear physics X-ray physics X-ray eergy spectroscopy LD Physics Leaflets P Ivestigatio of the characteristic spectra as a fuctio of the elemet's atomic umber: K-lies Objects of the experimet g Demostratio of x-ray fluorescece. g Recordig of x-ray fluorescece spectra of several elemets ad provig of Moseley's law for the K-lies of the characteristic spectrum. g Determiatio of the atomic screeig costat for the electros i the K-shells. Priciple Whe operatig the x-ray tube, i additio to the cotiuous bremsstrahlug, the characteristic radiatio is also emitted (see also e.g. Physics Leaflet P6.3.3.). I cotrast to the bremsstrahlug, the characteristic radiatio does ot possess a cotiuous distributio of radiatio itesity i the spectrum its spectrum is composed of sharp lies. The characteristic radiatio is geerated whe the electros which are accelerated towards the aode i the x-ray tube, kock other electros out of the ier shells of the atoms makig up the aode material. The atom ioised i this way the has a vacacy (electro hole) i a lower shell which previously had bee full. These electro holes ca be filled with electros from other, weaker boud shells of the atom: e.g. the K-shell ca be closed by the trasitio of a electro from the L-shell. Such a trasitio is coected with the emissio of a photo. This radiatio has oly particular discrete photo eergies correspodig to the eergy differece of the levels ivolved, ad it is characteristic for every chemical elemet. The desigatios of the characteristic x-ray lies are a combiatio of the symbol for the electro shell (K, L, M etc.) ad a Greek letter (α, β, γ etc.). The electro shell beig referred to is the oe which was ioised before the electro trasitio. For example the desigatio Kα-lie describes the trasitio from the L-shell ito the K-shell, Kβ refers to the trasitio from the M-shell to the K-shell. The Lα- ad Lβlies refer to the trasitios from the M-shell ad the N-shell to the L-shell. If viewed more closely, it becomes apparet that the historically developed omeclature of the x-ray lies is ot always logical. Fig. 1: Simplified termiology diagram of a atom demostratig the characteristic x-ray lies. I additio to the primary excitatio by the electros i the x- ray tube, the characteristic lies ca also be excited through the irradiatio of a target with high eergy photos. Here the ioisatio of the target atom is caused through the absorptio of a x-ray photo. This process of secodary excitatio is also called x-ray fluorescece. I order to calculate the eergies correspodig to the characteristic lies, the eergy levels i the atom (bidig eergies i the electro shells) have to be kow. These ca be treated i a similar way to hydroge by replacig the real charge of the ucleus Z by the effective charge Z = Z σ with a atomic screeig costat σ. eff Iv 006 LD Didactic GmbH. Leyboldstrasse 1. D Hürth. Phoe: (033) Fax: (033) ifo@ld-didactic.de LD Didactic GmbH Prited i the Federal Republic of Germay Techical alteratios reserved

2 P LD Physics Leaflets Apparatus 1 set of x-ray apparatus with Mo x-ray tube ad goiometer or 1 set of x-ray apparatus with Cu x-ray tube ad goiometer 1 x-ray eergy detector k-lies fluorescece target set CASSY sesor MCAbox CASSY Lab HF cable, 1 m PC with Widows 98/NT or higher Fig. : xperimetal setup: a collimator, b target, c target table, d detector. The eergy of a electro i a ier shell is the approximately represeted by a modified Bohr's formula with the pricipal quatum umber ad Z σ : ( Z σ ) = Rhc, with R beig the dberg costat, R = m e h c. The e 4 8ε 0 pricipal quatum umber refers to the electro shells: = 1 for the K-shell, = for the L-shell, = 3 for the M-shell etc. This formula describes the eergy structure of a electro i a ier shell. The atomic screeig costat σ i geeral depeds o ad Z. For the frequecies of the characteristic lies ν = 3 ( 1 ) h with the trasitios 1 ( > 1 ) the followig applies: ( Z σ ) ( Z σ ) 1 ν = cr. 1 If istead of σ 1 ad σ a sigle average atomic screeig costat σ, 1 is itroduced for the trasitios from to 1, this formula ca be re-writte as Moseley's law: ν ν R ( ) 1 1 Z σ,1 1 = with the dberg frequecy ν R =, (I) cr. This meas that the square root of the frequecy of the characteristic lies i oe series is a liear fuctio of the atomic umber Z. Rewritte to get the eergy of the characteristic lie, equatio (I) becomes: σ. (II) ( ) 1 1 Z,1 1 = Here the umerical value of is = Rhc 13.6 ev For the Kαlies of the lighter elemets (Z<30) the atomic screeig costat is σ 1 ad therefore ( ) = Z 1 3 4,1 (III). J With icreasig atomic umber, σ, 1 becomes smaller ad for Z 55 it eve becomes egative, i.e. at (?) these Z the ifluece of the outer electros exceeds the screeig effect of the ier electros. Set-up The experimetal set-up is show i fig.. - Push the coectio cable for the table-top device through the empty chael of the x-ray device ad coect it to the mii-din socket of the x-ray eergy detector. - Secure the sesor holder with the mouted x-ray eergy detector i the goiometer sesor arm. This x-ray apparatus fulfils all regulatios goverig the costructio of x-ray apparatus for use i schools ad fully protected devices for istructioal use, ad it is type approved for school use i Germay (NW 807 / 97 Rö). The built-i protectio ad screeig measures reduce the local dose rate outside the x-ray apparatus to less tha 1 µsv/h, a value which is of the same order of magitude as the atural backgroud radiatio. g Before commissioig the x-ray apparatus, ispect it for damage ad check that the high voltage is switched off whe the slide doors are opeed (see the operatig istructios for the x-ray apparatus). g Protect the x-ray apparatus from access by uauthorised people. Overheatig of the aode i the x-ray tube is to be avoided. g Whe switchig o the x-ray apparatus, check if the fa i the tube chamber is rotatig. The goiometer is positioed exclusively by meas of electric stepper motors. g Do ot block the target arm ad the sesor arm of the goiometer ad do ot use force to move them. LD Didactic GmbH. Leyboldstrasse 1. D Hürth. Phoe: (033) Fax: (033) ifo@ld-didactic.de LD Didactic GmbH Prited i the Federal Republic of Germay Techical alteratios reserved

3 LD Physics Leaflets P Coect the sigal output of the x-ray eergy detector to the BNC socket SIGNAL IN of the x-ray device by meas of the BNC cable icluded. - Feed eough coectio cable through to make complete movemet of the sesor arm possible. - Press the SNSOR butto ad set the sesor agle with the twist adjuster ADJUST maually to Coect sesor CASSY to the computer ad coect the MCA box. - Coect the SIGNAL OUT output i the coectio pael of the x-ray device to the MCA-box by meas of the BNC cable. - Set the distaces betwee the slit aperture of the collimator ad the axis of rotatio as well as betwee the axis of rotatio ad the widow of the x-ray eergy detector both to 5 to 6 cm. - Place the titaium (Ti) target from the K-lie fluorescece target set oto the target table. - Press the TARGT butto ad adjust the target agle maually usig the twist butto ADJUST to 45. Fig. 3b: X-ray fluorescece spectrum of iro (Fe). Carryig out the experimet - Coect the table-top power supply to the mais (after approx. mi the LD of the x-ray eergy detector will glow gree ad the device will be ready for use). - Call CASSY Lab ad set the measurig parameters "Multi-chael measuremet, 51 chaels, egative pulses, Gai = -.5, Measurig Time = 180 s". - Set the tube high voltage U = 35 kv, emissio curret I = 1 ma ad switch the high voltage o. - Start the spectrum recordig by clickig o or pressig F9. - The record spectra for the other targets i the target set for K-lie fluorescece. - Save the etire measuremet uder a suitable ame. xample of a measuremet From the example of a measuremet (fig. 3a-h), it is apparet that the eergy of the characteristic lies ad the separatio betwee the α-compoet ad the β-compoet of the K- spectrum series icreases with icreasig atomic umber. Fig. 3c: X-ray fluorescece spectrum of ickel (Ni). Fig. 3a: X-ray fluorescece spectrum of titaium (Ti). Fig. 3d: X-ray fluorescece spectrum of copper (Cu). LD Didactic GmbH. Leyboldstrasse 1. D Hürth. Phoe: (033) Fax: (033) ifo@ld-didactic.de LD Didactic GmbH Prited i the Federal Republic of Germay Techical alteratios reserved

P6.3.5.4-4 - LD Physics Leaflets Fig. 3e: X-ray fluorescece spectrum of zic (Z). Fig. 3h: X-ray fluorescece spectrum of silver (Ag).

4 P LD Physics Leaflets Fig. 3e: X-ray fluorescece spectrum of zic (Z). Fig. 3h: X-ray fluorescece spectrum of silver (Ag). valuatio ad results a) ergy calibratio of the spectra The eergy calibratio of the spectra is made for the Kα-lies of iro (Fe) ad molybdeum (Mo). - The spectra of iro ad molybdeum are to be selected i successio. - Ope the "ergy Calibratio" dialogue widow by pressig Alt+, select "Global ergy Calibratio" ad eter the eergies for the Fe Kα-lie (6.40 kev) ad the Mo Kα-lie (17.48 kev). - I the popup meu of the diagram widow select the meu item "Other valuatios" "Calculate Peak Ceter", select the Fe Kα-lie ad eter the result i the "ergy Calibratio" dialogue widow. - The determie the cetre for the Mo Kα-lie ad eter it. Fig. 3f: X-ray fluorescece spectrum of zircoium (Zr). b) Provig Moseley's law ad calculatio of the screeig costats For the quatitative aalysis, the eergies of the idividual lies are determied: - Select the eergy spectrum. - I the popup meu of the diagram widow call the meu item "Set Marker" "Vertical Lie" (Alt+S) ad approximately mark the positio of the Kα-lie ad the Kβ-lie. - I the popup meu of the diagram widow call the meu item "Other valuatios" "Gaussias of equal Width" ad mark the area of the desired peak (also mark sufficiet backgroud!). - Read the foud peak positios from the status lie ad eter them ito a table (see table 1). - For every lie calculate ad σ i, j accordig to equatio (II) ad eter them ito the table ( σ refers to the trasitio from = i to 1 = j ). i, j Fig. 3g: X-ray fluorescece spectrum of molybdeum (Mo). LD Didactic GmbH. Leyboldstrasse 1. D Hürth. Phoe: (033) Fax: (033) ifo@ld-didactic.de LD Didactic GmbH Prited i the Federal Republic of Germay Techical alteratios reserved

LD Physics Leaflets - 5 - P6.3.5.4 Tab. 1 xperimetally determied eergies of the K-lies ad the atomic screeig costats σ for the correspodig electro trasitios.

5 LD Physics Leaflets P Tab. 1 xperimetally determied eergies of the K-lies ad the atomic screeig costats σ for the correspodig electro trasitios. lemet Z, kev Kα-lie σ, kev, 1 i, j Kβ-lie σ 3, 1 - Ito the tables for the "Screeig " diagram eter atomic Ti Fe Ni Cu Z Zr Mo Ag Other evaluatios i the CASSY Lab cocerig Moseley's law: - Set up a ew variable "Atomic umber" (as parameter, symbol: Z, from: 0, to: 50, decimal places: 0). - Set up a ew variable "Moseley alpha" (as parameter, symbol: y_&a, from: 0, to: 50, decimal places: ). - Set up a ew variable "Moseley beta" (as parameter, symbol: y_&b, from: 0, to: 50, decimal places: ). - Set up a ew diagram called "Moseley" with the atomic umber as the x-axis ad y α, y β as the y-axis. - Ito the tables for the "Moseley" diagram eter atomic umber ad the values of ad the β-lies (as y β) (see fig. 4). for the α-lies (as y α) Fig. 4 Graphical represetatio of Moseley's law. xperimetal values of for the α-lies (y α, squares) ad the β-lies (as y β, triagles) ad the theoretical straight lie accordig to equatio (III). Compare the experimetally determied values with the theoretical values calculated usig equatio (III): - Select the "Moseley" diagram ad use Alt+F to ope the dialogue widow "Free fit". - ter equatio (III) as formula f(x,a,b,c,d) = (x- 1)*sqr(3/4). - Click "Cotiue with Rage Markig" ad select a umber of measurig poits i the diagram. Because the etered formula does ot iclude ay free parameters it will be displayed without ay fittig. The result is a theoretical straight lie calculated accordig to equatio (III) which correspods well to the measured values (see fig. 4). Other evaluatios i the CASSY Lab cocerig atomic screeig costats: - Set up a ew variable σ α (as parameter, ame: "Screeig alpha", symbol &s_&a, from: 0, to 3, decimal places: ). - Set up a ew variable σβ (as parameter, ame: "Screeig beta", symbol &s_&b, from: 0, to 3, decimal places: ). - Set up a ew diagram called "Screeig " with the atomic umber as the x-axis ad σ α, σ β as the y-axis. Fig. 5 ffective atomic screeig costats for the electro trasitios for the K-lies. umber ad the values of σ, 1 for the a-lies (as σ α) ad the ß-lies (as σ β) (see fig. 5). The values σ, 1 for the Kα-lies determied from experimetal values usig equatio (II) idicate that the deviatio from the theoretically expected σ=1 icreases with icreasig atomic umber Z. This is explaied by the fact that the ifluece of the exteral electros icreases as the umber of electros icreases. The screeig costats σ 3, 1 for the Kβ-lies have a value which idicates as expected a stroger effective screeig of the ucleus charge for the electro trasitios from the higher level = 3. LD Didactic GmbH. Leyboldstrasse 1. D Hürth. Phoe: (033) Fax: (033) ifo@ld-didactic.de LD Didactic GmbH Prited i the Federal Republic of Germay Techical alteratios reserved

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