Atomic and nuclear physics LEYBOLD Physics X-ray physics Leaflets P6.3.3.5 Physics of the atomic shell Edge absorption: filtering x-rays Objects of the experiment Recording the unfiltered spectrum of an x-ray tube and the spectrum filtered using as zirconium foil. Comparing the intensities of the characteristic lines in the filtered and unfiltered spectrum. Principles When x-rays pass through matter,they are attenuated by of the material thus increases abruptly as a function of the absorption and scattering of the x-ray quanta;the absorption wavelength at effect often predominates.This is due essentially to ionization of atoms,which release an electron from an inner shell,e.g. Ak=h.c (0 the K-shell.This can only occur when the quantum energy E=h.c 0 This abrupt change is known as the absorption edge,here the K-absorption edge. h:Planck's constant, c:velocity of light We must distinguish between the K-absorption edge and the characteristic x-radiation K and Kg emitted by the excited is greater than the binding energy Ek of the shell.The trans- atoms on the transition of an electron from a higher shell to the mission K-shell(see experiments P6.3.3.1 and P6.3.3.4).The relation- T入R ship o h.c R:intensity behind attenuator λ(Ka)= h·c Ro:intensity in front of attenuator Ek-EL andλKp=EK-w applies:thus Ak is shorter than A(K)and A(Kg).All three quantities depend on the atomic number Z of the absorbing (and emitting)atoms. Table1:Wavelengthsλ(K,),λ(Kg)andλ<for atomic numbers Z=40-42. Fig.1 Principle diagram of the transmission of an attenuator as a Element (K.) X(KB) K function of the x-ray wavelength pm pm pm Zr 40 78.74 70.05 68.88 Nb A1 74.77 66.43 65.31 Mo 42 71.08 63.09 61.99 Table 1 contains an excerpt of the relevant literature data [1]. P11.8060 The wavelength of the Kg radiation of molybdenum is below the K-absorption edge Ak of zirconium,and that of the K radiation is just above it.Mo-K radiation is thus only slightly attenuated in a zirconium foil,while Mo-Ke radiation is exten- sively absorbed.With the aid of zirconium foils,the charac- teristic x-radiation of an Mo anode can be filtered so that an approximately monochromatic beam is obtained behind the foil
Fig. 1 Principle diagram of the transmission of an attenuator as a function of the x-ray wavelength Atomic and nuclear physics X-ray physics Physics of the atomic shell LEYBOLD Physics Leaflets Edge absorption: filtering x-rays Objects of the experiment Recording the unfiltered spectrum of an x-ray tube and the spectrum filtered using as zirconium foil. Comparing the intensities of the characteristic lines in the filtered and unfiltered spectrum. Principles When x-rays pass through matter, they are attenuated by absorption and scattering of the x-ray quanta; the absorption effect often predominates. This is due essentially to ionization of atoms, which release an electron from an inner shell, e.g. the K-shell. This can only occur when the quantum energy E = h ⋅ c l (I) h: Planck’s constant, c: velocity of light is greater than the binding energy EK of the shell. The transmission T = R R0 (II) R: intensity behind attenuator R0: intensity in front of attenuator of the material thus increases abruptly as a function of the wavelength at lK = h ⋅ c EK (III) This abrupt change is known as the absorption edge, here the K-absorption edge. We must distinguish between the K-absorption edge and the characteristic x-radiation Ka and Kb emitted by the excited atoms on the transition of an electron from a higher shell to the K-shell (see experiments P6.3.3.1 and P6.3.3.4). The relationship l(Ka) = h ⋅ c EK − EL and l(Kb) = h ⋅ c EK − EM (IV) applies; thus lK is shorter than l(Ka) and l(Kb). All three quantities depend on the atomic number Z of the absorbing (and emitting) atoms. Table 1 contains an excerpt of the relevant literature data [1]. The wavelength of the Kb radiation of molybdenum is below the K-absorption edge lK of zirconium, and that of the Ka radiation is just above it. Mo-Ka radiation is thus only slightly attenuated in a zirconium foil, while Mo-Kb radiation is extensively absorbed. With the aid of zirconium foils, the characteristic x-radiation of an Mo anode can be filtered so that an approximately monochromatic beam is obtained behind the foil. Table 1: Wavelengths l(Ka), l(Kb) and lK for atomic numbers Z = 40−42. Element Z l(Ka) pm l(Kb) pm lK pm Zr 40 78.74 70.05 68.88 Nb 41 74.77 66.43 65.31 Mo 42 71.08 63.09 61.99 P6.3.3.5 0408-Ste 1
P6.3.3.5 LEYBOLD Physics Leaflets Apparatus 1X-ray apparatus.············ 554811 1 End-window counter fora,B,y and x-ray radiation·。。...· 55901 additionally required: 1 PC with Windows 9x/NT Fig.2 Schematic diagram of diffraction of x-rays at a monocrys- tal and 2 coupling between counter-tube angle and scat- This experiment measures the spectrum of an x-ray tube with tering angle (glancing angle) Mo anode,both unfiltered and filtered,using a zirconium foil. 1 collimator,2 monocrystal,3 counter tube A goniometer with NaCl crystal and a Geiger-Muller counter tube in the Bragg configuration are used to record the intensi- ties as a function of the wavelength.The crystal and counter tube are pivoted with respect to the incident x-ray beam in 2 coupling,i.e.the counter tube is turned at an angle twice as large as the crystal(see Fig.2). Setup In accordance with Bragg's law of reflection,the scattering angle in the first order of diffraction corresponds to the wavelength Setup in Bragg configuration: 入=2.d.sin8 0 Set up the experiment as shown in Fig.3.To set up the d=282.01 pm:lattice plane spacing of NaCl experiment,proceed as follows(see also the Instruction Sheet for the x-ray apparatus): Mount the collimator in the collimator mount(a)(note the guide groove). Safety notes Attach the goniometer to guide rods(d)so that the distance The x-ray apparatus fulfills all regulations governing an s between the slit diaphragm of the collimator and the x-ray apparatus and fully protected device for instructional target arm is approx.5 cm.Connect ribbon cable (c)for use and is type approved for school use in Germany(NW controlling the goniometer. 807/97Ro): Remove the protective cap of the end-window counter, The built-in protection and screening measures reduce the place the end-window counter in sensor seat (e)and con- local dose rate outside of the x-ray apparatus to less than nect the counter tube cable to the socket marked GM 1 uSv/h,a value which is on the order of magnitude of the TUBE. natural background radiation. By moving the sensor holder(b),set the distance s2 be- Before putting the x-ray apparatus into operation in- tween the target arm and the slit diaphragm of the sensor seat to approx.5 cm. spect it for damage and to make sure that the high voltage is shut off when the sliding doors are opened Mount the target holder with target stage. (see Instruction Sheet for x-ray apparatus) Loosen knurled screw (g).place the NaCl crystal flat on the Keep the x-ray apparatus secure from access by un- target stage (f),carefully raise the target stage with crystal authorized persons. all the way to the stop and carefully tighten the knurled screw(prevent skewing of the crystal by applying a slight pressure). Do not allow the anode of the x-ray tube Mo to overheat. If necessary,adjust the mechanical zero position of the When switching on the x-ray apparatus,check to make goniometer (see Instruction Sheet for x-ray apparatus). sure that the ventilator in the tube chamber is turning. Notes: The goniometer is positioned solely by electric stepper NaCI crystals are hygroscopic and extremely fragile. motors. Store the crystals in a dry place;avoid mechanical stresses on Do not block the target arm and sensor arm of the the crystal:handle the crystal by the short faces only. goniometer and do not use force to move them. If the counting rate is too low,you can reduce the distance s2 between the target and the sensor somewhat.However,the distance should not be too small,as otherwise the angular resolution of the goniometer is no longer sufficient to separate the characteristic K and Ke lines
This experiment measures the spectrum of an x-ray tube with Mo anode, both unfiltered and filtered, using a zirconium foil. A goniometer with NaCl crystal and a Geiger-Müller counter tube in the Bragg configuration are used to record the intensities as a function of the wavelength. The crystal and counter tube are pivoted with respect to the incident x-ray beam in 2q coupling, i.e. the counter tube is turned at an angle twice as large as the crystal (see Fig. 2). In accordance with Bragg’s law of reflection, the scattering angle q in the first order of diffraction corresponds to the wavelength l = 2 ⋅ d ⋅ sin q (V) d = 282.01 pm: lattice plane spacing of NaCl Setup Setup in Bragg configuration: Set up the experiment as shown in Fig. 3. To set up the experiment, proceed as follows (see also the Instruction Sheet for the x-ray apparatus): – Mount the collimator in the collimator mount (a) (note the guide groove). – Attach the goniometer to guide rods (d) so that the distance s1 between the slit diaphragm of the collimator and the target arm is approx. 5 cm. Connect ribbon cable (c) for controlling the goniometer. – Remove the protective cap of the end-window counter, place the end-window counter in sensor seat (e) and connect the counter tube cable to the socket marked GM TUBE. – By moving the sensor holder (b), set the distance s2 between the target arm and the slit diaphragm of the sensor seat to approx. 5 cm. – Mount the target holder with target stage. – Loosen knurled screw (g), place the NaCl crystal flat on the target stage (f), carefully raise the target stage with crystal all the way to the stop and carefully tighten the knurled screw (prevent skewing of the crystal by applying a slight pressure). – If necessary, adjust the mechanical zero position of the goniometer (see Instruction Sheet for x-ray apparatus). Notes: NaCl crystals are hygroscopic and extremely fragile. Store the crystals in a dry place; avoid mechanical stresses on the crystal; handle the crystal by the short faces only. If the counting rate is too low, you can reduce the distance s2 between the target and the sensor somewhat. However, the distance should not be too small, as otherwise the angular resolution of the goniometer is no longer sufficient to separate the characteristic Ka and Kb lines. Apparatus 1 X-ray apparatus . . . . . . . . . . . . . . 554 811 1 End-window counter for a, b, g and x-ray radiation . . . . . . . 559 01 additionally required: 1 PC with Windows 9x/NT Safety notes The x-ray apparatus fulfills all regulations governing an x-ray apparatus and fully protected device for instructional use and is type approved for school use in Germany (NW 807/97 Rö). The built-in protection and screening measures reduce the local dose rate outside of the x-ray apparatus to less than 1 mSv/h, a value which is on the order of magnitude of the natural background radiation. Before putting the x-ray apparatus into operation inspect it for damage and to make sure that the high voltage is shut off when the sliding doors are opened (see Instruction Sheet for x-ray apparatus). Keep the x-ray apparatus secure from access by unauthorized persons. Do not allow the anode of the x-ray tube Mo to overheat. When switching on the x-ray apparatus, check to make sure that the ventilator in the tube chamber is turning. The goniometer is positioned solely by electric stepper motors. Do not block the target arm and sensor arm of the goniometer and do not use force to move them. Fig. 2 Schematic diagram of diffraction of x-rays at a monocrystal and 2q coupling between counter-tube angle and scattering angle (glancing angle) 1 collimator, 2 monocrystal, 3 counter tube P6.3.3.5 LEYBOLD Physics Leaflets 2
LEYBOLD Physics Leaflets P6.3.3.5 Carrying out the experiment Start the software "X-ray Apparatus",check to make sure that the apparatus is connected correctly,and clear any existing measurement data using the button or the F4 key. Set the tube high voltage U=30.0 kV,the emission current /=1.O0 mA and the angular step width Aβ=0.1°. Press the COUPLED key to activate 20 coupling of target d and sensor and set the lower limit of the target angle to 4.2 and the upper limit to 8.3. Set the measuring time per angular step to At=5 s. Start measurement and data transfer to the PC by pressing the SCAN key. When the scan is finished,mount the zirconium foil sup- plied with your x-ray apparatus on sensor seat (e)of the ⑤ goniometer and start a new measurement by pressing the SCAN key. When you have finished measuring,save the measure- Fig.3 Experiment setup for investigating the filtration of x-rays ment series under an appropriate name by pressing the button or the F2 key. To display the measurement data as a function of the wavelength A,open the "Settings"dialog with the button or F5,and in the tab "Crystal",click on the button"Enter NaCl". Preparing the PC-based measurement: Connect the RS-232 output and the serial interface on your Measuring example PC(usually COM1 or COM2)using the 9-pin V.24 cable (supplied with x-ray apparatus). (see Fig.4) If necessary,install the software "X-ray Apparatus"under Windows 9x/NT(see Instruction Sheet for x-ray apparatus) and select the desired language. X-Ray Apparatus 回☒ 凸色路凸回色 Bragg Planck Transmission Moseley R 1/s K-alpha 2000 K-beta 1000 Fig.4 Diffraction spectrum of x-rays with the charac- teristic lines of the molyb denum anode in the wavelength range between 80 40 and 80 pm(U=30 kV) n pm Squares:not attenuated by Leybold Didactic GmbH,1998 Triangles:attenuated with zirconium foil 3
Preparing the PC-based measurement: – Connect the RS−232 output and the serial interface on your PC (usually COM1 or COM2) using the 9-pin V.24 cable (supplied with x-ray apparatus). – If necessary, install the software “X-ray Apparatus” under Windows 9x/NT (see Instruction Sheet for x-ray apparatus) and select the desired language. Carrying out the experiment – Start the software “X-ray Apparatus”, check to make sure that the apparatus is connected correctly, and clear any existing measurement data using the button or the F4 key. – Set the tube high voltage U = 30.0 kV, the emission current I = 1.00 mA and the angular step width Db = 0.18. – Press the COUPLED key to activate 2q coupling of target and sensor and set the lower limit of the target angle to 4.28 and the upper limit to 8.38. – Set the measuring time per angular step to Dt = 5 s. – Start measurement and data transfer to the PC by pressing the SCAN key. – When the scan is finished, mount the zirconium foil supplied with your x-ray apparatus on sensor seat (e) of the goniometer and start a new measurement by pressing the SCAN key. – When you have finished measuring, save the measurement series under an appropriate name by pressing the button or the F2 key. – To display the measurement data as a function of the wavelength l, open the “Settings” dialog with the button or F5, and in the tab “Crystal”, click on the button “Enter NaCl”. Measuring example (see Fig. 4) Fig. 3 Experiment setup for investigating the filtration of x-rays Fig. 4 Diffraction spectrum of x-rays with the characteristic lines of the molybdenum anode in the wavelength range between 40 and 80 pm (U = 30 kV) Squares: not attenuated Triangles: attenuated with zirconium foil LEYBOLD Physics Leaflets P6.3.3.5 3
P6.3.3.5 LEYBOLD Physics Leaflets Evaluation In the diagram,click the right mouse button to access the evaluation functions of the software"X-ray Apparatus"and select the command "Calculate Integral". Using the left mouse button,mark the peaks of the char- acteristic lines one after another and read their integral counting rate R in the bottom left corner of the diagram window. Calculate the ratio V of the Kg-radiation to the total char- acteristic radiation. R(KB) V=R(K)+R(Kg) Table 2:Integral counting rates of the characteristic lines and respective proportion of Kg-line. R(Ka) R(Kg) S-1 s-1 without Zr-Filter 4586 1288 0.22 with Zr-Filter 3897 137 0.034 Results The proportion of KB radiation making up the characteristic radiation of the Mo anode is significantly reduced when the zirconium foil is used.This means that: The characteristic radiation of the Mo anode is approximately monochromatized through absorption in a zirconium foil. Literature [1]C.M.Lederer and V.S.Shirley,Table of Isotopes,7th Edition,1978,John Wiley Sons,Inc.,New York,USA. LEYBOLD DIDACTIC GMBH.Leyboldstrasse 1.D-50354 Hurth.Phone (02233)604-0.Telefax(02233)604-222.Telex 17 223 332 LHPCGN D by Leybold Didactic GmbH Printed in the Federal Republic of Germany Technical alterations reserved
Evaluation – In the diagram, click the right mouse button to access the evaluation functions of the software “X-ray Apparatus” and select the command “Calculate Integral”. – Using the left mouse button, mark the peaks of the characteristic lines one after another and read their integral counting rate RI in the bottom left corner of the diagram window. – Calculate the ratio V of the Kb-radiation to the total characteristic radiation. V = Ri (Kb) Ri (Ka) + Ri (Kb) Results The proportion of Kb radiation making up the characteristic radiation of the Mo anode is significantly reduced when the zirconium foil is used. This means that: The characteristic radiation of the Mo anode is approximately monochromatized through absorption in a zirconium foil. Literature [1] C. M. Lederer and V. S. Shirley, Table of Isotopes, 7th Edition, 1978, John Wiley & Sons, Inc., New York, USA. Table 2: Integral counting rates of the characteristic lines and respective proportion of Kb-line. Ri (Ka) s − 1 Ri (Kb) s − 1 V without Zr-Filter 4586 1288 0.22 with Zr-Filter 3897 137 0.034 LEYBOLD DIDACTIC GMBH ⋅ Leyboldstrasse 1 ⋅ D-50354 Hürth ⋅ Phone (02233) 604-0 ⋅ Telefax (02233) 604-222 ⋅ Telex 17 223 332 LHPCGN D © by Leybold Didactic GmbH Printed in the Federal Republic of Germany Technical alterations reserved P6.3.3.5 LEYBOLD Physics Leaflets
