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1 NTRODUCTON (i) X-Rays was disovered by Prof. wilhelm Rontgen (895) for whih he was honoured with noble prize (90). (ii) They are also alled "Rontgen rays'. (iii) When high energeti athode rays (i.e. eletrons) strike a metal piee of high atomi weight and high melting point (e.g. W, M 0,...) a new kind of invisible rays are produed whih affet the photographi plate in the same way as do the light rays. Prof Rontgen named these unknown & invisible rays as X-rays. (iv) The X-rays are eletromagneti radiations with wavelengths from about 0. Å to 00 Å (0.0 nm to 0 nm). (These boundaries are not sharp, one an produe X-rays with 0.0 Å. (v) The shorter wavelength end of X-rays overlaps gamma rays region & the higher wavelength end overlaps with ultra violet region of the em spetrum. (vi) The frequeny range of X-rays is 0 6 Hz (soft) to 0 9 Hz (hard).the orresponding photon energy range is few hundred ev (soft) to few tenth of KeV (hard) thus X-rays onsists of high energy photons. (vii) The soft X-rays are those with wavelength greater than about 0 Å (0 Å 00 Å) while the hard rays are those with wavelength less than about 0 Å (0. Å 0 Å) PRODUCTON OF X-RAYS. A oolidge tube is used for the prodution of X-rays.. t ontains 3-major parts :- (A) Eletron Soure : Coolidge tube onsists of a athode C, whih is heated by a filament F through whih an eletri urrent is passed. Due to thermioni emission, eletrons are emitted by the athode. (B) Target: Target of high atomi weight and high melting point like tungsten or molybdenum is used whih is inlined to eletron beam at 5 0. Cold water is irulated to remove heat. (C) Battery : The potential differene between the athode & anode is 5 kv to 50 kv (for diagnosti X-rays). Cathode V + F C X-Rays Eletrons Evauated tube Target Coolent 3. Whole equipment is kept inside a hard glass bulb having a high vauum of about 0-6 m of merury (Hg).. Eletron is emitted by thermioni emission. 5. Thermioni emitted eletrons are aelerated by a potential differene of 0 5 volt towards target. 6. When aelerated eletrons strikes the target inlined at 5º & omes under sudden deeleration then emission of X-rays takes plae in the form of eletro magneti waves. 7. Atually only 0.% - % of energy of inident eletron takes part into prodution of X-rays. Rest onverts into heat. This auses target to beome very hot and so there is made some ooling arrangement. 8. Target is in form of wedge & hollow in shape. 9. The target is usually of tungsten while the rest of the anode is of opper (due to its high thermal ondutivity) 0. Properties of target meterial. (i) high melting point (ii) high thermal ondutivity (iii) high mehanial strength (iv) high atomi number z for more intense x-rays..the energy of x-rays photons or the penetrating power of the x-rays is ontrolled by the potential differene between the anode and the athode (i.e. on aelerating voltage). Higher is the aelerating voltage, higher is the KE of the bombarding eletrons and so higher is the energy of x-ray photons produed, or higher is the penetrating power of x-rays. A + Lead shield Page -

2 . The intensity of x-rays depends on the eletrons urrent. Greater is the number of eletrons emitted by the athode, more is the number of eletrons striking the target and so greater is the intensity of X-rays produed. 3. PROPERTES OF X-RAYS Properties of X-Rays may be divided into two headings :- 3. Properties similar to light :- () X-rays are eletromagneti waves with wavelength of the order of 0. nm ( Å) () The wavelength of X-rays is very small in omparison to the wavelength of light. Hene they arry muh more energy. (This the only differene between X-rays and light). (3) The wavelength of X-rays ranges from 00 to 0.A 0 where as that of visible light ranges from 000 to 7000A 0. () They are invisible. (5) They travel in straight line. (6) They travel with speed of light. (7) X-rays are not defleted by magneti and eletri field. X-rays arry no harge. (8) Wavelength of gama rays < wavelength of X-rays < Wavelength of ultra violet rays (9) They shows all the important properties of light rays, like ; refletion, refration, interferene, diffration and polarization et. (0)Due to this property they help in the study of rystal struture. ()They diffrat from rystal aording to bragg's law. d sin n, D sin n, where d distane between rystal latties glaning angle D distane between two onseutive atoms. ()They produe illumination on falling upon fluoresent material. 3. Properties similar to athode rays (a) They have ionisation power. Therefore when they passes through a gas, the gas is ionised. (b) They have penetration power. They penetrate through dif f erent depth into dif f erent substane, e.g. wood, ardboard, thin metal sheet, flesh et. Penetration power depends upon wavelength of x-rays and nature of material. f Penetration power ( energy ) f Penetration power ( energy ) () X-rays do not pass through heavy metal (Lead, Calium, Barium Sulphate) and bones. f suh objets is plaed in their path, they ast their shadow. (d) They affet photographi plates. (e) They show photoeletri effet and ompton effet. (f) Long exposure to X-rays is injurious for human body. (g) When x-rays falls on living reatures, it produes strain. Ex. Maximum distane between intermoleular lattie planes of a rystal is 0 Å. Wavelength of diffrated x-rays by this rystal will be- (A) 0 Å (B) 0 Å (C) 30 Å (D) 0 Å Sol. max ( d sin) n min max 0 Å max. ABSORPTON OF X-RAYS 0 sin90º () W hen X-rays passes through medium, intensity of X-rays dereases. () f is the initial intensity of X-rays then intensity after traveling x distane in medium will be e -x where ntensity of inident X-Ray photon ntensity of transmitted X-Ray photon x Thikness of given sheet Absorption or attenuation oeffiient for given sheet material Graph of v/s x Page -

3 (3) Absorption of X-rays is high in heavy material but low in light material. () Absorber of X-rays are Pb, BaSO. (5) Pb is best absorber for X -rays Ex. Sol. (6) High of X -rays more absorption () Low of X -rays less absorption beause low (7) Half value thikness or Half width (x / ) t is the thikness of given sheet that redues the intensity of inident X-ray photon by 50% When x x / then x & e X n () x x / (8) Absorption oeffiient () e x f x then e 0 e.78 So when x 0 then x e Absorption oeffiient for a given material is equal to inverse of that thikness that redues the intensity of transmitted x-ray to 37% of its original value. The attenuation oeffiient of aluminium for sof t x-rays is.73 per m. Then the perentage of these x-rays that would be transmitted by an aluminium sheet m thik is nearly- (A) 8 % (B) 37 % (C) 63 % (D) 30 % e x e e e % K i 5. CLASSFCATON OF X-RAYS X-ray emitted from target an be divided in two ategories. (A) Continuous X-ray (B) Charateristis X-ray As the eletron enters into the target material, it reading loses its kineti energy & may ome to rest inside the metal. The eletron before finally being stopped, makes several ollisions with the atoms in the target. At eah ollision one of the following two types of X-rays may get form. 5. Continuous x-ray : mv When high energy eletrons (aelerated by oolidge tube potential) strike the target element they are defieted by oulomb attration of nuleus & due to numerous glaning olisions with the atoms of the target, they lose energy whih appears in the form of eletromagneti waves (bremsstrahlung or braking radiation) & the remaining part inreases the kineti energy of the olliding partiles of the target. The energy reelved by the olliding partiles goes into heating the target. The eletron makes another ollision with its remaining energy Bremsstrahlung e v K L M e v. When high energeti eletrons enter into target material, they are deelerated. n this proess emission of energy take plae. Spetrum of this energy is ontinuous. This is also alled Bremstrahlung.. Continuous x-rays are also alled deelerated radiations. 3. Continuous spetrum (or ) depends upon potential differene between filament and target.. t does not depends upon nature of target material. 5. f V is the potential differene & is the frequeny of emitted x-ray photon then. h x-ray photon K f K i energy lost by eletron in striking with target element K f mv' Page - 3

4 Case() When inident eletron loses its omplete energy in st ollision with target atom then photon of maximum frequeny (or minimum wavelength) will be emitted & in this ase ev mv h max min min v min, max max ev ev h Case () When inident eletron do not loses any of its energy in ollision with target atom. ev mv h 0 and therefore Wavelength of ontinuous x-ray photon ranges from ertain minimum to infinity & therefore x-ray spetrum is not monohromati. 5. Charateristis x-rays : We shall now disuss what happens if the eletron knoks out an inner eletron from the atom with whih it ollides. (i) The eletrons in an atom oupy different quantum states haraterized by the quantum numbers n,, m, m s. The energy primarily depends on the priniple quantum number n. (ii) The two eletrons orresponding to n are said to be in K shell, those orresponding to n are in L shell et. (iii) Suppose, the inident eletron knoks out an eletron from the K shell. This will reate a vaany in the K shell in the sense that now there is only one eletron with n, whereas two oluld be aommodated by Pauli exlusion priniple. An eletron from a higher energy state may make a transition to this vaant state. When suh a transition takes plae, the differene of energy E is onverted into an X-ray photon of wavelength / E. (iv) X-rays emitted due to eletroni transition from a higher energy state to a vaany areated in the K shell are alled K series X-rays. e inident eletron (v) As the eletrons in K shell are most tightly bound, maximum energy is to be given to the atom to knok out an eletron from the K shell. That is why, in figure, the energy level of the atom with a vaany in the K shell is shown highest. The energies E K, E L... et. are harateristi properties of the material. For different materials, the values of these energies will be different. The values of E K E L, E L E M et. also have definite values for a given material. The wavelengths of the X-rays emitted orresponding to these transitions are k k L E K E L E K E M E L E M k-eletron h K a X-ray Page -

5 et. These wavelength, therefore, have definite values for a partiular material. The X-rays emitted in this way are the harateriti X-rays shown in figure. They are so named beause their wavelengths may be used to identify the element from whih they originate. (vi) Charatenisti x-rays spetrum is a line spetrum. (vii) n this spetrum frequeny or wavelength of lines of series do not hanges with aelerating voltage. (viii) k 6 z Å (ix) Properties of harateristi x-ray is regulated by atomi number of target element, not by oolidge tube potential. (x) E K K h K K K K E + E L h + h L K + L K + L K (xi) For the same target element 7 K 3 K K K L L (xii)graph of ntensity of harateristi X-rays versus wavelengths The X-ray emission when stream of fast moving eletrons strike a target of heavy element., orresponds to harateristi X-rays. Ex.3 (xiii) Different targets of tungsten ( W). M olybdenum ( M o) and hromium (Cr) are used and the kineti energies of the inident eletrons are kept onstant. t is observed that the minimum wavelength m in is independent of target material. The potential differene between the athode and the target in a oolidge tube is 0 KV. What an be the minimum wavelength (in Å) of the x-rays emitted by this tube. What will be the momentum of this photon- (A) 0.0 Å, kg m/s (B) 0. Å, kg m/s (C) 0. Å, kg m/s (D) 0.0 Å, kg m/s Ex. Sol.(C) W hen eletrons aelerated through a potential differene V strike a target, the maximum frequeny of the emitted x-rays is given byev h max min min min ev min m 0. Å The momentum of the emitted x-ray photon is p h min p kg m/s The maximum frequeny of the x-ray emitted by an x-ray tube operating at 30 KV is- (A) Hz (C) Hz 8 (B) Hz (D) Hz Page - 5

6 Sol.(C) 9 3 ev h Ex.5 Sol.(A) min Hz f the x-ray tube is working at 5 KV then the minimum wavelength of x-rays will be (A) 0.9 Å (B) 0.9 Å (C) 0.9 Å (D) 0.39 Å 00 Å V 00 min MOSELEY'S LAW 0.9 Å () n 93, Moseley did experiments on then known elements & alulated the K frequenies of the various elements. (ii) This law exhibits relation between frequeny of harateristi X-rays & atomi number Z of target element. (iii) Moseley noted that the harateriti lines shifted systematially as the target material is hanged. (iv) Aording to this low square root of frequeny of harateristi X-rays is proportional to atomi number Z. Z (v) The moseley s experimental studies (a) Supported Bohr s theory (b) Experimentally determined the Z of elements () Established the importane of ordering of elements in periodi table by atom numbers & not by atomi weight (The obalt nikel an arrangement) (d) Gaps in Moseley s data for z 3, 6, 7, 75 suggested existene of new elements whih were later disovered. (e) The graph between & Z or energy of X-ray photon E h versus Z for harateristi X-ray lines is paraboli as shown in fig. Z K K (f) The atomi number of Cu, Ag & Pt were established to be 9, 7 & 78 respetively. (vi) When an eletron in n level is ejeted, then for the remaining eletron the eletri field due to nuleus is sreened by the remaining eletron in the n level. (vii) Moseley estimated that the effetive nulear harged for the K transition is (Z ) e. (viii)aording to Bohr s model, the energy released during the transition from n to n is given by E h K RCh Z eff K K 3RC 3RC a (Z b) (Z ) (Z ) where a & b depend on transition & do not depend on target material. a O 3RC.7 x 0 5 Hz b sreening onst. for K X-ray line b for L X-ray line b X-RAY DOZE. Doze of X-ray are measured in terms of produed ions or free energy via ionisation.. These are measured in Rontgen 3. Rontgen do not measure energy but it measures ionization power.. Safe doze for human body per week is one Rontgen. 5. One Rontgen is the amount of X-rays whih emits (.5 x 0 J) free energy through ionization of gram air at NTP. Z Page - 6

7 8. USES OF X-RAYS Medial uses - The X-rays quite freely pass through the flesh but are stopped by the bones. So we an photograh the bones inside the body on a photographi film. This is used to detet and study bone fratures due to an aident. Chest radiograph are used to study diseases in lungs. Dentist also use X-rays to study teeth-deay. X-ray are also use in aner therapy. These damage the tumour ells. Uses in Art and Siene X-rays are used to detet overed paintings. t is also used for determining rystal strutures. Struture of DNA was also determined using X-ray diffration. Uses in industry X-rays have been used to detet minute raks and faults in onrete and metal struture whih otherwise are not visible. X-rays have been used as a quality ontrol in rubber industry (e.g.) if there are bubble in rubber tyres, X-rays will indiate it. X-ray mahines are used to inspet suitases, wooden boxes et, without opening them and an be typially found at the ustom, seurity ounters at airports et. 9. PONT S T O REMEMBER () The value of min depends upon the voltage V of the X-ray tube. () For the prodution of X-rays, it is essential to keep high order vauum in the tube. (3) The intensity and the penetrating power of X-rays obtained by a oolidge tube may be ontrolled independently. () Roentgen disovered X-rays. (5) Only 0.0 % energy of eletrons is utilised for the prodution of x-rays. (6) Wavelengths of K-series are generally less than A 0 and those of L-series are nearly 0 times longer. (7) X-rays show photoeletri effet. (8) f the number of eletrons striking the target is inreased, the intensity of x-rays produed will also be inreased. (9) Soft x-rays are produed at omparatively low potential differene and high pressure. (0) Moseley's law relates frequeny & atomi number. () The wavelength of x-rays is of the order of 0 0 m. () The target element in an x-ray tube must have a high atomi number and melting point. (3) X-rays an be used to study the struture of rystals. () Coolidge x-ray tube is the modifiation of Roentgen's x-ray tube. (5) Coolidge x ray tube ats as an automati retifier. (6) The reverse phenomenon of x-rays is known as photo eletri effet. (7) Diffration of x-rays was first verified by Von Lave spots. (8) Eletrons are emitted by making x-rays inident on the surfae of matter where as x-rays are produed by making high energy eletrons inident on target material. (9) The diffration of x-rays is not possible by ordinary grating beause the size of grating element is muh larger than the wave length of x-rays. (0) () () m m V V E E Z Z (for ontinuous x-ray) (for harateristi x-ray) () H and He atom an not emit x-ray beause energy level are very lose in these atom. () Patients are asked to drink BaSO solution for x-ray examination beause BaSO is good absorber of x-rays. (3) X-ray an not be used in Radar beause it does not reflet bak. () X-ray photography works on prinipal of shadow photography. (5) Prodution of x-ray and photo eletri effet are opposite phenomenon beause in photo eletri effet photon energy is transfer to eletrons and in ase of x-ray prodution eletron's kineti energy is transferred to photon. Page - 7

8 (6) To observe diffration of x-rays, diffration grating should be order of x-ray's wavelength. Simple hole is not order of that so it does not show diffration but distane between rystal planes are the order of wavelength of x-rays so we an see diffration pattern from target with the help of the rystal. (7) A random and exess exposure to x-ray may indue disease, x-rays have a damaging effet on the living ells of body whih may lead to ell death. High exposure for a long period (say for years) may lead to aner or geneti defets. (8) E K 0. (z ) ev Page - 8

9 Ex. The ratio of energies of x-rays of the wavelength 0.0Å and 0.5 Å will be- (A) : (B) : (C) : 5 (D) 50 : Sol.(D) Ex. Sol.(A) V E E. E 50 E When the minimum wavelength of x-rays is Å then the applied potential differene between athode and antiathode will be- (A) 6. KV (B).8 KV (C).8 KV (D) 6 KV 00 min (Å) Volt V KV Ex.3 An x-ray tube is operated at 5 KV. Calulate the upper limit of the speed of the eletrons striking the target. (A) m/s (B) m/s (C) m/s (D) m/s Sol.(A) The maximum kineti energy of an eletron aelerated through a potential differene of Ex. Sol.(B) v max Ex.5 V volt is mv ev maximum veloity v v ev m v m/s An x-rays tube is being operated at 0 KV, the maximum speed of eletrons striking the antiathode will be- (A) 8. m/s (B) m/s (C). 0 7 m/s (D) zero ev m v max m/s SOLVED EXAMPLES 0 0 When x-rays of wavelength 0.5 Å would transmitted by an aluminium tube of thikness 7 mm, its intensity remains one-fourth. The attenuation oeffiient of aluminium for these x-rays- (A) 0.88 mm (B) 0.89 mm (C) 0.98 mm (D) None 3 Sol.(C) 0, x 7mm (given).303 log 0 x.303 log mm Ex.6 The separation between Bragg's planes in a rystal is 0 Å. Then the maximum wavelength of those x-rays whih an be diffrated by this rystal is- (A) 5 Å (B) 0 Å (C) 0 Å (D) 0. Å Sol.(C) d sin n Ex.7 max ( dsin ) max nmin dsin 90º 0 Å max 0Å An x-ray tube with Cu target is operated at 5 KV. the glaning angle for a NaCl. Crystal for the Cu k line is Find the wavelength of this line.( d f or NaCl.8 Å, h erg-se) (A) 3.06 Å (B).53 Å (C) 0.75 Å (D) None Sol.(B) Aording to Brag law, d sin n, n for first order.8 sin A 0 Ex.8 The maximum kineti energy of the eletrons hitting a target so as to produe x-ray of wavelength Å is (A). KeV (B). KeV (C) KeV (D) None Sol.(B) min Å (given) Ex.9 min Thus, E 0 (ev) (nm) E 0(eV)(nm).0(nm) 00 ev E. KeV Eletrons are aelerated in television tubes through potential differene of about 0 KV. Lowest wavelength & highest frequeny of the x-rays emitted will be- Page - 9

10 (A). Å,. 0 8 Hz Ex.3 (B). Å,. 0 8 Hz (C). Å,. 0 8 Hz (D). Å,. 0 8 Hz 00 Sol.(D) min Å. Å 0000 The wavelength of K -line harateristi x-rays emitted by an element is 0.3 Å. The wavelength of k -line emitted by the same element will be- (A) 0.7 Å (B) 0.3 Å (C) 0.39 Å (D) 0.9 Å Ex.0 Sol.(A) Ex. max min Hz. m m V m V Å When the x-ray tube is operated at KV, then x-rays of minimum wavelength 6. Å are produed. f the tube is operated at 0 KV, then the minimum wavelength of x-rays will be- (A) 0.6 Å (B) 6. Å (C) 3. Å (D) zero The short wavelength limit of ontinuous x-radiation emitted by an x-ray tube operating at 30 KV is 0. Å. Calulate Plank's onstant- (A) erg-se (B) erg-se (C) J-se (D) J-se h Sol.(D) min ev h h 3 0 ev min h J-se 8 0 Ex. What element has k line of wavelength.785 Å. R m -. (A) Platinum (B) Zin (C) Ferrus (D) Cobalt Sol.(D) For k line (Z ) 3 k R (Z ). k R (Z ) Z 6 Z 7 Thus, the element is obalt Sol.(A) Ex. Sol. Ex.5 R (Z b) R (Z b) Å f the k radiation of Mo (Z ) has a wavelength of 0.7 A 0. Calulate the wavelength of the orresponding radiation of Cu (Z 9). From Mosley's law, we have, (Z ) (Z ) A where A is some onstant, (ZMO ) (Z ) Cu Cu 0.7 Cu MO 8 or k 8.5 A 0 Cu 0.7 What is the energy of k x-ray photon of opper (Z 9)? (A) 7.99 KeV (B) 8.9 KeV (C) 8.5 KeV (D) 7.9 KeV Sol.(A) E(k ) 0. (Z ) ev kev 8 KeV Page - 0

Physics 30 Lesson 32 x-rays and the Compton Effect

Physics 30 Lesson 32 x-rays and the Compton Effect I. Disovery of x-rays Physis 30 Lesson 32 x-rays and the Compton ffet During all the researh on athode rays, several sientists missed their hane at some glory. Hertz narrowly missed disovering x-rays during