Outline 24. QUANTUM PHYSICS. Liew Sau Poh. Objectives. Objectives. Objectives. Objectives Photon. Objectives

Transcription

1 Outlie 4. QUNTUM PHYSICS Liew Sau Poh 4. Photos 4. Wave-particle duality 4.3 tomic structure 4.4 X-rays 4.5 Naosciece Objectives (a) describe importat observatios i photoelectric emissio experimets (b) recogise features of photoelectric emissio that caot be explaied by wave theory ad explai these features usig the cocept of quatisatio of light (c) use the equatio for a photo E= hf (d) explai the meaig of work fuctio ad threshold frequecy Objectives (e effect, hf=w + ½mv max (f) uderstad the meaig of stoppig potetial ad use ev s = ½mv max (h) use the relatio = h/p to calculate de Broglie wavelegth (i) iterpret the electro diffractio patter as a evidece of the wave ature of electro Objectives (j) explai the advatages of a electro microscope as compared to a optical microscope (l) derive a expressio for the radii of the orbits (m) derive the formula Objectives () explai the productio of emissio lie spectra with referece to the trasitios betwee eergy levels (o) explai the cocepts of excitatio eergy ad ioisatio eergy (p) iterpret X-ray spectra obtaied from X-ray tubes (q) explai the characteristic lie spectrum ad cotiuous spectrum icludig mi i X-rays Objectives (r) derive ad use the equatio mi = hc / ev (s) describe X-ray diffractio by two parallel adjacet atomic plaes d si = m (u) explai the basic cocept of aosciece (v) state the applicatios of aosciece i electroics devices 4. Photo Photoelectric effect: Whe electromagetic radiatio is icidet to the surface of a metal, electros are ejected from the surface. Photoelectros: The electros emitted by this effect. UV Visible light Visible light Photoelectros Photoelectros No photoelectros Metals Metals other tha lkali Metals lkali Metals

2 Photo packet or budle of eergy is called a photo. hc Eergy of a photo is E = hf = where h f is the frequecy of the radiatio or photo, c is the speed of light (e.m. wave) ad is the wavelegth. Properties of photos photo travels at a speed of light c i vacuum. (i.e. 3 x 8 m/s) It has zero rest mass. i.e. the photo ca ot exist at rest. E h The kietic mass of a photo is, m = c = c E h The mometum of a photo is, p = = c Photos travel i a straight lie. Eergy of a photo depeds upo frequecy of the photo; so the eergy of the photo does ot chage whe photo travels from oe medium to aother. Properties of photos Wavelegth of the photo chages i differet media; so, velocity of a photo is differet i differet media. Photos are electrically eutral. Photos may show diffractio uder give coditios. Photos are ot deviated by magetic ad electric fields. Photoelectric Effect UV Photoelectros Metals Visible light Visible light No photoelectros Photoelectros lkali Metals Metals other tha lkali Metals Photoelectric Effect The pheomeo of emissio of electros from maily metal surfaces exposed to light eergy (X rays, rays, UV rays, Visible light ad eve Ifra Red rays) of suitable frequecy is kow as photoelectric effect. The electros emitted by this effect are called photoelectros. The curret costituted by photoelectros is kow as photoelectric curret. Note: No metals also show photoelectric effect. Liquids ad gases also show this effect but to limited extet. Experimetal (Photoelectric Effect) UV light W C + + C Metallic cathode K V Metallic ode W Quartz Widow - Photoelectro Experimetal (Photoelectric Effect) Glass trasmits oly visible ad ifra-red lights but ot UV light. Quartz trasmits UV light. Whe light of suitable frequecy falls o the metallic cathode, photoelectros are emitted. These photoelectros are attracted towards the +ve aode ad hece photoelectric curret is costituted. Experimetal (Photoelectric Effect) ) Effect of Itesity of Icidet Light o Photoelectric Curret: For a fixed frequecy, the photoelectric curret icreases liearly with icrease i itesity of icidet light. I Itesity (L)

3 Experimetal (Photoelectric Effect) ) Effect of Potetial o Photoelectric Curret: For a fixed frequecy ad itesity of icidet light, the photoelectric curret icreases with icrease i +ve potetial applied to the aode. Whe all the photoelectros reach the plate, curret becomes maximum ad is kow as saturatio curret. V S I Saturatio Curret L L L > L + Potetial of (V) Experimetal (Photoelectric Effect) ) Effect of Potetial o Photoelectric Curret: Whe the potetial is decreased, the curret decreases but does ot become zero at zero potetial. This shows that eve i the absece of acceleratig potetial, a few photoelectros maage to reach the plate o their ow due to their K.E. V S I Saturatio Curret L L L > L + Potetial of (V) Experimetal (Photoelectric Effect) ) Effect of Potetial o Photoelectric Curret: Whe ve potetial is applied to the plate w.r.t. C, photoelectric curret becomes zero at a particular value of ve potetial called stoppig potetial or cut-off potetial. Itesity of icidet light does ot affect the stoppig potetial. V S I Saturatio Curret L L L > L + Potetial of (V) Experimetal (Photoelectric Effect) 3) Effect of Frequecy of Icidet Light o Photoelectric Curret: For a fixed itesity of icidet light, the photoelectric curret does ot deped o the frequecy of the icidet light. Because, the photoelectric curret simply depeds o the umber of photoelectros emitted ad i tur o the umber of photos icidet ad ot o the eergy of photos. V S I Saturatio Curret > + V S Potetial of (V) Experimetal (Photoelectric Effect) 4) Effect of Frequecy of Icidet Light o Stoppig Potetial: For a fixed itesity of icidet light, the photoelectric curret icreases ad is saturated with icrease i +ve potetial applied to the aode. However, the saturatio curret is same for differet frequecies of the icidet lights. V S I Saturatio Curret > + V S Potetial of (V) Experimetal (Photoelectric Effect) 4) Effect of Frequecy of Icidet Light o Stoppig Potetial: Whe potetial is decreased ad take below zero, photoelectric curret decreases to zero but at differet stoppig potetials for differet frequecies. V S I Saturatio Curret > + V S Potetial of (V) Higher the frequecy, higher the stoppig potetial. i.e. VS 5) Threshold Frequecy The graph betwee stoppig potetial ad frequecy does ot pass through the origi. It shows that there is a miimum value of frequecy called threshold frequecy below which photoelectric emissio is ot possible however high the itesity of icidet light may be. It depeds o the ature of the metal emittig photoelectros. V S (V) 8. Cocept of light quatisatio

4 Laws of Photoelectric Emissio For a give substace, there is a miimum value of frequecy of icidet light called threshold frequecy below which o photoelectric emissio is possible, howsoever, the itesity of icidet light may be. The umber of photoelectros emitted per secod (i.e. photoelectric curret) is directly proportioal to the itesity of icidet light provided the frequecy is above the threshold frequecy. Laws of Photoelectric Emissio The maximum kietic eergy of the photoelectros is directly proportioal to the frequecy provided the frequecy is above the threshold frequecy. The maximum kietic eergy of the photoelectros is idepedet of the itesity of the icidet light. The process of photoelectric emissio is istataeous. i.e. as soo as the photo of suitable frequecy falls o the substace, it emits photoelectros. The photoelectric emissio is oe-to-oe. i.e. for every photo of suitable frequecy oe electro is emitted. the eergy of the photo is absorbed by the electro ad is used i two ways: part of eergy is used to overcome the surface barrier ad come out of the metal surface. This part work fuctio ). The remaiig part of the eergy is used i givig a to the maximum kietic eergy of the photoelectros ( ½ mv max ccordig to law of coservatio of eergy, hf = + ½ mv max = hf + ½ mv Photo h max ½ mv max = h ( f - f ) Photoelectro = h Metal ½ mv max Verificatio of Laws of Photoelectric Emissio based Verificatio of Laws of Photoelectric Emissio based ½ mv max = h ( - ) If <, the ½ mv max is egative, which is ot possible. Therefore, for photoelectric emissio to take place >. Sice oe photo emits oe electro, so the umber photoelectros emitted per secod is directly proportioal to the itesity of icidet light. ½ mv max = h ( - ) It is clear that ½ mv max as h ad are costat. This shows that K.E. of the photoelectros is directly proportioal to the frequecy of the icidet light. Photoelectric emissio is due to collisio betwee a photo ad a electro. s such there ca ot be ay sigificat time lag betwee the icidece of photo ad emissio of photoelectro. i.e. the process is istataeous. The delay is oly -8 secods. pplicatio of Photoelectric Effect utomatic fire alarm utomatic burglar alarm Scaers i Televisio trasmissio Reproductio of soud i ciema film I paper idustry to measure the thickess of paper To locate flaws or holes i the fiished goods I astroomy To determie opacity of solids ad liquids utomatic switchig of street lights To cotrol the temperature of furace Photometry Beauty meter To measure the fair complexio of ski Light meters used i ciema idustry to check the light Photoelectric sortig Photo coutig Meteorology Photoelectric Threshold Photo eergy: 5 Photo i Bidig Eergies K: L: 5 M: Which shells are cadidates for photoelectric iteractios?

5 Photoelectric Threshold Photoelectric Threshold Photo eergy: 5 NO NO Bidig Eergies K: L: 5 M: Photo eergy: 5 Bidig Eergies K: L: 5 M: NO Photo i Which shells are cadidates for photoelectric iteractios? Photo i Which shells are cadidates for photoelectric iteractios? Photoelectric Threshold Photoelectric Threshold Photo eergy: 5 YES NO Bidig Eergies K: L: 5 M: Photo eergy: 5 Bidig Eergies K: L: 5 M: P.E. ~ eergy 3 NO Photo i Which shells are cadidates for photoelectric iteractios? Photo i B Photo eergy: Which photo has a greater probability for photoelectric iteractios with the m shell? Photoelectric Threshold Photoelectric Threshold Photo eergy: 55 Bidig Eergies K: L: 5 M: Photo eergy: 55 YES YES Bidig Eergies K: L: 5 M: Photo i Which shells are cadidates for photoelectric iteractios? NO Photo i Which shells are cadidates for photoelectric iteractios? Photoelectric Threshold Photoelectric Threshold Photo eergy: 5 Bidig Eergies K: L: 5 M: Photo eergy: 5 YES YES Bidig Eergies K: L: 5 M: Photo i Which shells are cadidates for photoelectric iteractios? YES Which shells are cadidates for photoelectric iteractios?

6 Photoelectric Threshold P.E. ~ eergy 3 Photoelectric Threshold Whe photo eergy just reaches bidig eergy of ext (ier) shell, photoelectric iteractio ow possible with that shell shell offers ew cadidate target electros Photoelectric iteractios decrease with icreasig photo eergy Photo eergy: 49 YES NO YES Photo eergy: 5 YES Bidig Eergies K: 5 L: 5 Photoelectric Threshold Whe photo eergies just reaches bidig eergy of ext (ier) shell, photoelectric iteractio ow possible with that shell, where shell offers ew cadidate target electros Iteractio Probability M-shell iteractios possible L-shell bidig eergy Photo Eergy K-shell bidig eergy L-shell iteractios possible K-shell iteractio s possible Photoelectric Threshold causes step icreases i iteractio probability as photo eergy exceeds shell bidig eergies Iteractio Probability L-edge K-edge Photo Eergy Dual Nature of Radiatio ad Matter 4. Wave-particle Duality Wave theory of electromagetic radiatios explaied the pheomeo of iterferece, diffractio ad polarizatio. O the other had, quatum theory of e.m. radiatios successfully explaied the photoelectric effect, Compto effect, black body radiatios, X- ray spectra, etc. Thus, radiatios have dual ature. i.e. wave ad particle ature. Dual Nature of Radiatio ad Matter Louis de Broglie suggested that the particles like electros, protos, eutros, etc have also dual ature. i.e. they also ca have particle as well as wave ature. Note: I o experimet, matter exists both as a particle ad as a wave simultaeously. It is either the oe or the other aspect. i.e. The two aspects are complemetary to each other. His suggestio was based o: The ature loves symmetry. The uiverse is made of particles ad radiatios ad both etities must be symmetrical. de Broglie wave ccordig to de Broglie, a movig material particle ca be associated with a wave. i.e. a wave ca guide the motio of the particle. The waves associated with the movig material particles are kow as de Broglie waves or matter waves.

7 Expressio for de Broglie wave ccordig to quatum theory, the eergy of the photo is E = h = hc the photo is So = h mc E = mc or = h p where p = mc is mometum of a photo If istead of a photo, we have a material particle of mass m movig with velocity v, the the equatio becomes which is the expressio for de Broglie wavelegth. h = mv Coclusio de Broglie wavelegth is iversely proportioal to the velocity of the particle. If the particle moves faster, the the wavelegth will be smaller ad vice versa. If the particle is at rest, the the de Broglie wavelegth is ifiite. Such a wave ca ot be visualized. de Broglie wavelegth is iversely proportioal to the mass of the particle. The wavelegth associated with a heavier particle is smaller tha that with a lighter particle. de Broglie wavelegth is idepedet of the charge of the particle. = h mv The Compto Effect Let the light is made up of particles (photos), ad that photos have mometum, with eergy hf collides with a statioary electro. Some of the eergy ad mometum is trasferred to the electro (this is kow as the Compto effect), but both eergy ad mometum are coserved (elastic collisio). fter the collisio the photo has eergy hf ad the electro has acquired a kietic eergy K. Coservatio of eergy: hf = hf + K = h mv Matter waves, similar to electromagetic waves, ca travel i vacuum ad hece they are ot mechaical waves. Matter waves are ot electromagetic waves because they are ot produced by accelerated charges. Matter waves are probability waves, amplitude of which gives the probability of existece of the particle at the poit. Coclusio Davisso ad Germer Experimet beam of electros emitted by the electro gu is made to fall o Nickel crystal cut alog cubical axis at a particular agle. The scattered beam of electros is received by the detector which ca be rotated at ay agle. V C F Nickel Crystal Electro Gu Crystal Lattice Davisso ad Germer Experimet The eergy of the icidet beam of electros ca be varied by chagig the applied voltage to the electro gu. Itesity of scattered beam of electros is foud to be maximum whe agle of scatterig is 5 ad the acceleratig potetial is 54 V. V C F Nickel Crystal Electro Gu Crystal Lattice Davisso ad Germer Experimet = 8 i.e. = 65 For Ni crystal, lattice spacig d =.9 Å For first pricipal maximum, = Electro diffractio is similar to X-ray diffractio. V C dsi = gives F Electro Gu Crystal Lattice Nickel Crystal =.65 Å Icidet Beam Icidet Beam Itesity of scattered beam at 44 V = 5 Itesity of scattered beam at 54 V hypothesis, = h mev or Icidet Beam Icidet Beam.7 Å = V Itesity of scattered beam at 48 V Itesity of scattered beam at 64 V de Broglie wavelegth of movig electro at V = 54 Volt is.67 Å which is i close agreemet with.65 Å.

8 Itesity vs Diffractio patter after electros Diffractio patter after 3 electros The Electro Microscope Usig wave-ature ad particle ature of electro Electro is accelerated through a high voltage Better tha optical microscope Shorter Wavelegth : (up to - ) vs (- 7 ) Higher resolvig power: aometer vs. micro Diffractio patter after 7 electros 4.3 tomic structure Early models of atom I 898, Joseph Joh Thomso suggested a model of a atom that cosists of homogeous positively charged spheres with tiy egatively charged electros embedded throughout the sphere as show i the Figure. positively charged sphere electro atom SF7 66 The electros much likes currats i a plum puddig. atom. I 9, Erest Rutherford performed a critical correct ad proposed his ew atomic model kow show i Figure pictured as electros orbitig aroud a cetral ucleus which cocetrated of positive charge. The electros are acceleratig because their directios are costatly chagig as they circle the ucleus. ucleus electro ucleus electro

9 Based o the wave theory, a acceleratig charge emits eergy. Hece the electros must emit the EM radiatio as they revolve aroud the ucleus. s a result of the cotiuous loss of eergy, the radii of the electro orbits will be decreased steadily. This would lead the electros spiral ad falls ito the ucleus, hece the atom would collapse as show i Figure. +Ze e +Ze e eergy loss eergy loss. Oly certai discrete orbits (statioary states) are allowed for the electro. Electro i a statioary state does ot radiate 3. Classical mechaics apply to electro i a statioary state (ot betwee states) 4. Whe a electro moves from oe SS to aother, a chage i eergy occurs ivolvig the emissio (or absorptio) of a sigle photo of frequecy v = E/h 5. Permitted orbits (SS) are those i which agular mometum ca take o oly the discrete values h/ force as the cetripetal force he obtaied v e 4 m e 4 (4 ) h I 93, Neils Bohr proposed a ew atomic model based o hydroge atom. assumes that each electro moves i a circular orbit which is cetred o the ucleus, the ecessary cetripetal force beig provided by the electrostatic force of attractio betwee the positively charged ucleus ad the egatively charged electro. +e r F e e v O this basis he was able to show that the eergy of a orbitig electro depeds o the radius of its orbit. This model has several features which are described by the postulates (assumptios) stated below :. The electros move oly i certai circular orbits, called STTIONRY STTES or ENERGY LEVELS. Whe it is i oe of these orbits, it does ot radiate eergy.. The oly permissible orbits are those i the discrete set for which the agular mometum of the electro L equals a iteger times h/. Mathematically, L h ad L m vr h : pricipalquatum umber,, 3,... r:radius of theorbit m:massof theelectro mvr (.) where 3. Emissio or absorptio of radiatio occurs oly whe a electro makes a trasitio from oe orbit to aother. The frequecy f of the emitted (absorbed) radiatio is give by E hf E f E i where E :chageof eergy h: Plack' s costat :fialeergy state :iitialeergy state E f E i If E f > E i If E f < E i bsorptio of EM radiatio Emissio of EM radiatio

10 Eergy level of hydroge atom + r e Cosider oe electro of charge e ad mass m moves i a circular orbit of radius r aroud a positively charged ucleus with a velocity v. The electrostatic force betwee electro ad ucleus cotributes the cetripetal force as write i the relatio below: electrostatic force 4 Fe F c QQ mv r r e mv 4 r cetripetal force ad Q Q e (.3) F e v e mvr h By takig square of both side of the equatio, we get h m v r (.4) 4 By dividig the eqs. (.4) ad (.3), thus m v mv r r h 4 e 4 h me r ad 4 k electrostatic costat me which r is radii of the permissible orbits for the where a is called the atom. r r h a 4 r 4 k h mke a ad h ; 4 mke,,3... (.6) of hydroge (.5) the radius of the most stable (lowest) orbit or groud state (=) i the hydroge atom ad its value is a Uit coversio: a m The radii of the orbits associated with allowed orbits or states are 4a,9a, thus the radii are quatized OR.53 Å (agstrom) Å =. m Eergy level i hydroge atom is defied as a fixed eergy correspodig to the orbits i which its electros move aroud the ucleus. The eergy levels of atoms are quatized. The total eergy level E of the hydroge atom is give by Potetial eergy of the electro E U K (.7) Kietic eergy of the electro Eergy level i hydroge atom Potetial eergy U of the electro is give by kq Q r ke U where Q e; Q e ucleus electro U (.8) a ad r a Kietic eergy K of the electro is give by K mv e but mv 4 r e K where 4 r 4 ke K a Therefore the eq. (.7) ca be writte as E ke a ke a k (.9) ke E (.) a ad r a I geeral, the total eergy level E for the atom is ke Z E (.) a where Z : a to m ic u m b e r Usig umerical value of k, e ad a, thus the eq. (.) ca be writte as Note: E ev ev;,,3,... t h : e ergy le v el o f s tate (o rb it) E (.) where E Eqs. (.) ad (.) are valid for eergy level of the hydroge atom.

11 The egative sig i the eq. (.) idicates that work has to be doe to remove the electro from the boud of the atom to ifiity, where it is cosidered to have zero eergy. The eergy levels of the hydroge atom are whe =, the groud state (the state of the lowest eergy level) ; 3.6 E ev 3. 6 ev 3.6 =, the first excited state; E ev 3. 4 ev 3.6 E =3, the secod excited state; 3 ev. 5 ev E 4 ev. 85 ev =4, the third excited state; 4 =, the eergy level is 3.6 E ev Lie spectrum electro is completely removed from the atom. The emissio lies correspod to the photos of discrete eergies that are emitted whe excited atomic states i the gas make trasitios back to lower eergy levels. Figure.4 shows diagrammatically the various eergy levels i the hydroge atom. E (ev ) Figure.4. Free electro th excited state rd excited state 3. 5 d excited state Ioizatio eergy is defied as the eergy required 3. 4 st excited state by a electro i the groud state to escape Excitatio eergy completely from is defied as the eergy the attractio of required by a electro that the ucleus. raises it to a excited state from its groud state. atom becomes io. Lie spectrum 3. 6 Groud state excited state is defied as the eergy levels that higher tha the groud state. is defied as the lowest stable eergy state of a atom. Figure below shows lie spectra produced by emissio i the visible rage for hydroge (H), mercury (Hg) ad eo (Ne). Figure.5 Hydroge Spectrum = 656, 486, 434, 4 & 397 m, what is the patter? Hydroge emissio lie spectrum Emissio processes i hydroge give rise to series, which are sequeces of lies correspodig to atomic trasitios. The series i the hydroge emissio lie spectrum are Lyma series ivolves electro trasitios that ed at the groud state of hydroge atom. It is i the ultraviolet (UV) rage. Balmer series ivolves electro trasitios that ed at the st excited state of hydroge atom. It is i the visible light rage. Hydroge emissio lie spectrum The series i the hydroge emissio lie spectrum are Pasche series ivolves electro trasitios that ed at the d excited state of hydroge atom. It is i the ifrared (IR) rage. Brackett series ivolves electro trasitios that ed at the 3 rd excited state of hydroge atom. It is i the IR rage. Pfud series ivolves electro trasitios that ed at the 4 th excited state of hydroge atom. It is i the IR rage. Figure below shows diagrammatically the series of hydroge emissio lie spectrum E (ev ). Free electro Pfud series th excited state rd excited state Brackett series. 5 d excited state Pasche series Balmer series Lyma series st excited state Stimulatio. 3.6 Groud state

12 i the Bohr model of a hydroge atom. Wavelegth of hydroge emissio lie spectrum If a electro makes a trasitio from a outer orbit of level i to a ier orbit of level f, thus the eergy is radiated. The eergy radiated i form of EM radiatio (photo) where the wavelegth is give by E hc E hc Wavelegth of hydroge emissio lie spectrum E hc ca be writte as hc E E f E hc rd postulate, the eq. (.3) i where E ad f E i ke a ke a f i hc hc ke a ke a f f f ke hca i i ad ke a ke hca i RH R H (.4) f i where R H : Rydberd's costat.97 f : fial value of i : iitialvalueof 7 m For the hydroge lie spectrum, Lyma series( f = ) Balmer series( f = ) Pasche series( f =3 ) Brackett series( f =4 ) Pfud series( f =5 ) R H R H R H R H R H Note: i i i i i To calculate the shortest wavelegth i ay series, take i = predicts successfully the eergy levels of the hydroge atom but fails to explai the eergy levels of more complex atoms. ca explai the spectrum for hydroge atom but some details of the spectrum caot be explaied especially whe the atom is placed i a magetic field. Figure.7 No magetic field Trasitios Magetic field Eergy Levels Spectra 4.4 X-ray caot explai the Zeema effect Zeema effect is defied as the splittig of spectral lies whe the radiatig atoms are placed i a magetic field. Trasitios No magetic field Magetic field Eergy Levels Spectra

13 Review: toms Smallest particle of matter that has the properties of a elemet. Cotais a small, dese, positively charged ceter (ucleus). Nucleus surrouded by a egative cloud of electros. Electros revolve i fixed, well-defied orbits (eergy levels). Review: toms 3 Fudametal Particles of a tom Electro Proto Neutro toms Electros ca oly exist i certai shells that represet electro bidig eergies K, L, M shells (K is closest to the ucleus) The closer a electro is to the ucleus, the higher the bidig eergy (stregth of attachmet to the ucleus). toms I their ormal state, atoms are electrically eutral If a atom has a extra electro or has had a electro removed, it has bee ioized. How X-rays are Created To produce x-rays, you eed 3 thigs:. source of electros. force to move them rapidly 3. Somethig to stop them rapidly *ll 3 coditios met i a x-ray tube Early X-ray Tube Early X-ray Tube

14 The X-Ray tube is the sigle most importat compoet of the radiographic system. It is the part that produces the X-rays History of X-ray ad XRD Wilhelm Corad Rötge discovered X-Rays i Nobel prize i Physics Wilhelm Corad Rötge (845-93) moder radiograph of a had Early use of X-Rays Withi few moths of their discovery, X-rays were beig put to practical use. This is a X-ray of bird shot embedded i a had. Ufortuately, much of the early use of X-rays was far too aggressive, resultig i later cacer. History of X-ray ad XRD Radiographs like the oes i the last slide are simply shadowgrams. The X-rays either pass straight through or are stopped by the object. The diagram o the upper left illustrates the priciple ad shows a perfect shadow. Sectio 9.4 History of X-ray ad XRD History of X-ray ad XRD I reality, a large fractio of the X-rays are ot simply absorbed or trasmitted by the object but are scattered. The diagram o the bottom left illustrates this effect ad illustrates the fuzzy edge of the object that is produced i the image by the scattered X-rays. Max vo Laue (897-96) The first kid of scatter process to be recogised was discovered by Max vo Laue who was awarded the Nobel prize for physics i 94 "for his discovery of the diffractio of X-rays by crystals". His collaborators Walter Friedrich ad Paul Kippig took the picture o the bottom left i 9. It shows how a beam of X-rays is scattered ito a characteristic patter by a crystal. I this case it is copper sulphate. History of X-ray ad XRD What are X-rays? Max vo Laue (897-96) The X-ray diffractio patter of a pure substace is like a figerprit of the substace. The powder diffractio method is thus ideally suited for characterizatio ad idetificatio of polycrystallie phases. Beams of electromagetic radiatio Short wavelegth, high eergy Wave (siusoidal, oscillatig electric field with, at right agles to it, a magetic field) wavelegth frequecy Particle (photo) Photo eergy E E = h (h -34 Js) Iteracts with electros!

15 Properties of a wave Electromagetic radiatio Wave = c / (c=3. km/s) Å (Ågström) is o-si uit of legth X-rays: -8 to - m Å = - m =. to Å. m dimesio of atoms, bods, uit- X-Rays Electromagetic radiatio with short wavelegths Wavelegths less tha for ultraviolet Wavelegths are typically about. m X-rays have the ability to peetrate most materials with relative ease High eergy photos which ca break chemical bods dager to tissue Discovered ad amed by Roetge i 895 X-Rays X-rays (discovered ad amed by Roetge): electromagetic radiatio with short typically about. m wavelegths X-rays have the ability to peetrate most materials with relative ease X-rays are produced whe high-speed electros are suddely slowed dow Wilhelm Corad Rötge How are X-rays geerated?. Radioactive materials udergo decay (too may uclear particles or too high eutro/proto ratio) 5 3 P -> 6 3 S + X-ray How are X-rays geerated?. Machies X-ray tube (accelerates electros which iteract with electros of target) Particle accelerator e- X-ray tube X-rays 3. Electros iteract with target (aode), Target (Co, Cu) producig X-rays Two types of X-radiatio are produced: Bremsstrahlug radiatio), produces a cotiuous spectrum of X- ray wavelegths Electro beam Tugste Filamet. Electros are accelerated i electric field. W filamet is heated, electros

16 Two types of X-radiatio are produced:. Characteristic Radiatio (X-rays of distict wavelegths, uique for each elemet) a) Icomig electro kocks ier shell electro out of its place b) Empty site is filled by a electro from a higher shell Two types of X-radiatio are produced:. Characteristic Radiatio (X-rays of distict wavelegths, uique for each elemet) a) The differece i bidig eergy betwee ier ad outer shell electros is released as X-ray of characteristic wavelegth Typical X-ray spectrum Cotiuous radiatio = Bremsstrahlug radiatio Characteristic radiatio is used i XRD, which requires moochromatic radiatio (eg. CuK =.548 Å) Productio of X-rays X-rays are produced whe high-speed electros are suddely slowed dow Ca be caused by the electro strikig a metal target curret i the filamet causes electros to be emitted Productio of X-rays These freed electros are accelerated toward a dese metal target The target is held at a higher potetial tha the filamet Productio of X-rays (Bremsstrahlug) electro passes ear a target ucleus ad is deflected from its path by its attractio to the ucleus This produces a acceleratio of the electro ad hece emissio of electromagetic radiatio Productio of X-rays (Bremsstrahlug) If the electro loses all of its eergy i the collisio, the iitial eergy of the electro is completely trasformed ito a photo The wavelegth the is e V mi h hc e V max hc mi Productio of X-rays (Bremsstrahlug) Not all radiatio produced is at this wavelegth May electros udergo more tha oe collisio before beig stopped This results i the cotiuous spectrum produced

17 Characteristic X-Rays Whe a metal target is bombarded by high-eergy electros, x-rays are emitted The x-ray spectrum typically cosists of a broad cotiuous spectrum ad a series of sharp lies The lies are depedet o the metal of the target The lies are called characteristic x-rays Characteristic X-Rays The details of atomic structure ca be used to explai characteristic x-rays bombardig electro collides with a electro i the target metal that is i a ier shell If there is sufficiet eergy, the electro is removed from the target atom The vacacy created by the lost electro is filled by a electro fallig to the vacacy from a higher eergy level The trasitio is accompaied by the emissio of a photo whose eergy is equal to the differece betwee the two levels X-ray Spectrum The x-ray spectrum has two distict compoets ) Bremsstrahlug: a cotiuous broad spectrum, which depeds o voltage applied to the tube ) The sharp, itese lies, which deped o the ature of the target material Productio of Characteristic Radiatio The X-ray Productio X-rays are emitted whe high eergy electros or ay other charged particles bombard a metal target. The X-ray spectrum typically cosists of a broad cotiuous bad cotaiig a series of sharp lies. The cotiuous spectrum is a result of collisio betwee icomig electros ad the target atoms. The sharp lies are a result of the removal of ier shell electros of the target atoms. Possible Iteractio Betwee Electro Beam ad the Target The X-ray Spectrum Some Features of the Spectrum The eergy of Bremsstrahlug radiatio rage from zero to a maximum value which depeds o the potetial differece applied o the tube. The itesity of the low eergy photos withi the spectrum is reduced because the absorptio of the target material. The average eergy of the X-ray beam is about oe third of the maximum. The sharp lies, K,L,M etc stay at the same positios. The lie X-ray ca be produced oly whe the icomig electros exceed some values.

18 moder Diffractometer X-ray tube sample Detector 3. X-ray diffractio The X-ray diffractometer = d si Experimet of Laue 9 X-ray diffractio by a sigle crystal Powder diffractometer with Bragg-Bretao geometry. alyst cotrols (choice of target i X-ray tube) (positios of X-ray tube / sample / detector What is X-ray diffractio? Scatterig pheomeo, X-rays passig through crystal tool for the characterisatio of solid materials based o their crystal structure Used by Earth Scietists Chemists Physicists Material Scietists rchaeologists What is XRD used for? Idetificatio of mierals Quatificatio of mierals Determiatio of crystal structure Uit-cell dimesios, symmetry, atom Determiatio of grai sizes, strai Typical samples Mierals, rocks, corals, shells Rosalid E. Frakli 95 What is X-ray diffractio? XRD complemets other aalytical methods Visual Need large crystals! cm Optical microscopy (colour, birefrigece, Iteractio of X-rays with crystal structures Crystal structure: three-dimesioal, periodic arragemet of atoms i space. Uit-cell of NaCl µm to mm Na Cl SEM (compositio: wt.% SiO What about polymorphs? (Calcite, ragoite = CaCO 3 ) > 3 µm XRF (compositio: wt.% SiO What about polymorphs? (Calcite, ragoite = CaCO 3 ) May differet layers of atoms exist i a crystal structure. Each set of layers has a distict iterplaar distace (d-spacig).

19 Iteractio of X-rays with crystal structures X-rays (electromagetic wave) iteract with the electros of the atoms i the crystal Coheret Scatter: elastic collisio betwee a photo (Xray) ad ad electro (i crystal) - outgoig photos (X-ray) have same wavelegth, frequecy ad eergy as icomig photos [XRD!] Icoheret Scatter (= Compto scatter): ielastic collisio betwee photo ad electro - outgoig photos have lower eergy Iteractio of X-rays with a scatterig ceter Iterferece Icomig wave Every electro/atom i structure acts as a scatterig ceter, ad is a source of spherical waves of the same wavelegth ad frequecy as the icomig wave. Positive Iterferece Negative Iterferece X-rays passig through a crystal lattice X-rays out of phase! Crests ad troughs add up ad form a wave with twice the amplitude. Crests ad troughs are offset ad cacel each other out. This happes to most X-rays scattered i crystals due to the large umber of scatterig ceters... Diffractio X-rays i phase! some X-rays to experiece positive (or costructive) iterferece i crystals. This is called diffractio. = d hkl si radiatio coheretly, the cocerted costructive iterferece at specific agles is called diffractio Diffractio i crystallie materials is best described with = d hkl si Diffractio of X-rays by Crystals For diffractio to occur, the spacig betwee the grooves must be approximately equal to the wavelegth of the radiatio to be measured For X-rays, the regular array of atoms i a crystal ca act as a threedimesioal gratig for diffractig X-rays For positive iterferece to occur, the path-differece must be equal to oe wavelegth ( or multiple wavelegths (. Schematic for X-ray Diffractio beam of X-rays with a cotiuous rage of wavelegths is icidet o the crystal The diffracted radiatio is very itese i certai directios These directios correspod to costructive iterferece from waves reflected from the layers of the crystal The diffractio patter is detected by photographic film d hkl hkl

20 Photo of X-ray Diffractio Patter The array of spots is called a Laue patter The crystal structure is determied by aalyzig the positios ad itesities of the various spots This is for NaCl The beam reflected from the lower surface travels farther tha the oe reflected from the upper surface If the path differece equals some itegral multiple of the wavelegth, costructive iterferece occurs gives the coditios for costructive iterferece X-Ray Diffractio Bragg Equatio d si = ( )/d Costructive iterferece: dsi m d.5m i NaCl For =.7m dsi Crystal solid such as sodium st maximum will be at = agle of icidece = wavelegth d = iterplae distace of crystal X-ray Bragg Equatio Whe the X-rays strike a layer of a crystal, some of them will be reflected. We are iterested i X-rays that are i-phase with oe aother. X-rays that add together costructively i x-ray diffractio aalysis i-phase before they are reflected ad after they reflected. Icidet agle Reflected agle Wavelegth of X-ray Total Diffracted gle Bragg Equatio These two x-ray beams travel slightly differet distaces. The differece i the distaces traveled is related to the distace betwee the adjacet layers. Coectig the two beams with perpedicular lies shows the differece betwee the top ad the bottom beams. The lie CE is equivalet to the distace betwee the two layers (d) DE d si The legth DE is the same as EF, so the total distace traveled by the bottom wave is expressed by: EF d si DE d si DE EF d si d si Costructive iterferece of the radiatio from successive plaes occurs whe the path differece is a itegral umber of waveleghts. This is the Bragg Law. Bragg Equatio d where, d is the spacig of the plaes ad is the order of diffractio. Bragg reflectio ca oly occur for wavelegth d si This is why we caot use visible light. No diffractio occurs whe the above coditio is ot satisfied. The diffracted beams (reflectios) from ay set of lattice plaes ca oly occur at particular agles pradicted by the Bragg law.

21 rthur Holly Compto Discovered the Compto effect Worked with cosmic rays Director of the lab at U of Chicago Shared Nobel Prize i 97 The Compto Effect Compto directed a beam of x-rays toward a block of graphite He foud that the scattered x-rays had a slightly loger wavelegth that the icidet x-rays This meas they also had less eergy The amout of eergy reductio depeded o the agle at which the x-rays were scattered The chage i wavelegth is called the Compto shift Compto Scatterig Compto assumed the photos acted like other particles i collisios Eergy ad mometum were coserved The shift i wavelegth is o h ( cos ) m c e Compto Scatterig The quatity h/m e c is called the Compto wavelegth Compto wavelegth =. 43 m Very small compared to visible light The Compto shift depeds o the scatterig agle ad ot o the wavelegth Experimets cofirm the results of Compto scatterig ad strogly support the photo cocept Three-Dimesioal Coformal Radiatio Therapy (3D-CRT) Tumors usually have a irregular shape Three-dimesioal coformal radiatio therapy (3D-CRT) uses sophisticated computers ad CT scas ad/or MRI scas to create detailed 3-D represetatios of the tumor ad surroudig orgas Three-Dimesioal Coformal Radiatio Therapy (3D-CRT) Radiatio beams are the shaped exactly to the size ad shape of the tumor Because the radiatio beams are very precisely directed, earby ormal tissue receives less radiatio exposure Sample We are choosig icomig agle = outgoig agle. Therefore oly diffractio from atomic plaes i the crystal structure that are parallel to the flat sample surface are detected For example, if we aalysed this sigle muscovite muscovite crystal with XRD, lyig flat o the sample holder with its plae, oly () plaes would diffract. Powder X-ray Diffractio sample () Sample However, we wat LL crystallographic plaes to cotribute to the XRD patter. ll samples eed to be groud up very fiely (ideally - µm grai size), ad the grais orieted radomly i the muscovite sample holder. sample () Powder X-ray Diffractio

22 4.5 Naosciece Naosciece refers to the ability to maipulate idividual atoms ad molecules, makig it possible to build machies o the scale of huma cells. Naotechology Naotechology is the uderstadig ad cotrol of matter at dimesios of roughly to aometers. Naotechology ivolves imagig, measurig, modelig, ad maipulatig matter at this legth scale. Naoscale t the aoscale, the physical, chemical, ad biological properties of materials differ i fudametal ad valuable ways from the properties of idividual atoms ad molecules or bulk matter. Naotechology R&D is directed toward uderstadig ad creatig improved materials, devices, ad systems that exploit these ew properties Facts aometer is oe billioth of a meter. I 5 the US govermet spet a estimated $,8 millio While difficult to measure accurately, some have estimated that worldwide govermet fudig has icreased to about five times what it was i 997, exceedig $ billio i. CMOS TECHNOLOGY (released March 4): 5 millio trasistors 9 m desig rules 3.4 GHz clock frequecy DRM chips: 4 Gb chips demostrated (~ 9 trasistors/cm) Now chips based o the desig rules of m are o the way. - 3 m) processor I 4 we were Itroductio already iside aotechology! 78 Oe area of aotechology R&D is medicie. Medical researchers work at the micro- ad ao-scales to develop ew drug delivery methods, therapeutics ad pharmaceuticals. For a bit of perspective, the diameter of DN, our geetic material, is i the.5 aometer rage, while red blood cells are approximately.5 micrometers. pplicatios/products limited), aoparticles are beig used i a umber of idustries. Naoscale materials are used i electroic, magetic ad optoelectroic, biomedical, pharmaceutical, cosmetic, eergy, catalytic ad materials applicatios. reas producig the greatest reveue for aoparticles reportedly are chemical-mechaical polishig, magetic recordig tapes, suscrees, automotive catalyst supports, biolabelig, - Naotechology has the potetial to profoudly chage our ecoomy ad to improve our stadard of livig, i a maer ot ulike the impact made by advaces over the past two decades by iformatio techology. It is quite possibly the ext step i techology that will lead to great iovatios. If the capabilities of aosciece are fully haressed, aythig could be possible.

23 Numerous products featurig the uique properties of aoscale materials are available to cosumers ad idustry today. Most computer hard drives, for istace, cotai giat magetoresistace (GMR) heads that, through ao-thi layers of magetic materials, allow for a sigificat icrease i storage capacity. Other electroic applicatios iclude o-volatile magetic memory, automotive sesors, ladmie detectors ad solid-state compasses Naomaterials Examples are aoscale particles, tubes ad rods. Naoparticles Naorods Naotube Some other uses Bur ad woud dressigs Water filtratio Catalysis detal-bodig aget Step assists o vas. Coatigs for easier cleaig glass Bumpers ad catalytic coverters o cars Protective ad glarereducig coatigs for eyeglasses ad cars Suscrees ad cosmetics. Loger-lastig teis balls. Light-weight, stroger teis racquets. Stai-free clothig ad mattresses. Ik. Medical uses The pharmaceutical ad chemical idustries are beig impacted greatly by aotechology, as well. New commercial applicatios of aotechology that are expected i two to five years i these idustries iclude: advaced drug delivery systems, icludig implatable devices that automatically admiister drugs ad sesor drug levels ad medical diagostic tools, such as cacer taggig mechaisms. Bibliography ex.jsp x.html _area=