ATOMIC STRUCTURE. electron

Transcription

1 J-Physics VRIOUS MODL S FOR STRUCTUR OF TOM TOMIC STRUCTUR Dalto' s Theory very material is composed of miute particles kow as atom. tom is idivisible i.e. it caot be subdivided. It ca either be created or be destroyed. ll atoms of same elemet are idetical physically as well as chemically, whereas atoms of differet elemets are differet i properties. The atoms of differet elemets are made up of hydroge atoms. (The radius of the heaviest atom is about times that of hydroge atom ad its mass is about 5 times that of hydroge). The atom is stable ad electrically eutral. Thomso' s tom Model The atom as a whole is electrically eutral because the positive charge preset o the atom (sphere) is equal to the egative charge of electros preset i the sphere. tom is a positively charged sphere of radius m i which electros are embedded i betwee. The positive charge ad the whole mass of the atom is uiformly distributed throughout the sphere. electro positively charged matter Shortcomigs of Thomso' s model (i) The spectrum of atoms caot be explaied with the help of this model (ii) Scatterig of particles caot be explaied with the help of this model RUTHRFORD TOM MODL Rutherford experimets o scatterig of particles by thi gold foil The experimetal arragemet is show i figure. particles are emitted by some radioactive material (poloium), kept iside a thick lead box. very fie beam of particles passes through a small hole i the lead scree. This well collimated beam is the allowed to fall o a thi gold foil. While passig through the gold foil, particles are scattered through differet agles. zic sulphide scree was placed out the other side of the gold foil. This scree was movable, so as to receive the particles, scattered from the gold foil at agles varyig from to 8. Whe a particle strikes the scree, it produces a flash of light ad it is observed by the microscope. It was foud that : OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 lead box source of -particle lead scree vacuum beam of -particle gold foil 7 m about i 8 is repelled back ZS scree microscope some are deviated through large agle most -pass through ( ) 4 ( ) cosec 9 8

2 J-Physics Most of the particles wet straight through the gold foil ad produced flashes o the scree as if there were othig iside gold foil. Thus the atom is hollow. Few particles collided with the atoms of the foil which have scattered or deflected through cosiderable large agles. Few particles eve tured back towards source itself. The etire positive charge ad almost whole mass of the atom is cocetrated i small cetre called a ucleus. The electros could ot deflected the path of a particles i.e. electros are very light. lectros revolve roud the ucleus i circular orbits. So, Rutherford 9, proposed a ew type of model of the atom. ccordig to this model, the positive charge of the atom, istead of beig uiformly distributed throughout a sphere of atomic dimesio is cocetrated i a very small volume (Less tha 3 m is diameter) at it cetre. This cetral core, ow called ucleus, is surrouded by clouds of electro makes. The etire atom electrically eutral. ccordig to Rutherford scatterig formula, the umber of particle scattered at a agle by a target are give by t(ze ) 4 6(4 ) r (mv ) si Where umber of particles that strike the uit area of the scatter umber of target atom per m 3 t Thickess of target Z e Charge o the target ucleus e Charge o particle r Distace of the scree from target v Velocity of particles at earer distace of approach the size of a ucleus or the distace of earer approach is give by r (Ze) (Ze) 4 4 K mv where K K.. of particle b area b target ucleus electro ucleus + -particle r + ucleus Ze Bohr' s tomic Model I 93 eils Bohr, a Daish Physicist, itroduced a revolutioary cocept i.e., the quatum cocept to explai the stability of a atom. He made a simple but bold statemet that "The old classical laws which are applicable to bigger bodies caot be directly applied to the sub atomic particles such as electros or protos. Bohr icorporated the followig ew ideas ow regarded as postulates of Bohr's theory.. The cetripetal force required for a ecirclig electro is provided by the electrostatic attractio betwee the ucleus ad the electro i.e. Ze e mv 4 r r...(i) bsolute permittivity of free space 8.85 C m r m Mass of electro + v Velocity (liear) of electro ucleus r Radius of the orbit i which electro is revolvig. +Ze Z tomic umber of hydroge like atom. v lectro OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

3 J-Physics. lectros ca revolve oly i those orbits i which agular mometum of electro about ucleus is a itegral multiple of h h. i.e., mvr...(ii) Pricipal quatum umber of the orbit i which electro is revolvig. 3. lectros i a atom ca revolve oly i discrete circular orbits called statioary eergy levels (shells). electro i a shell is characterised by a defiite eergy, agular mometum ad orbit umber. While i ay of these orbits, a electro does ot radiate eergy although it is accelerated. 4. lectros i outer orbits have greater eergy tha those i ier orbits. The orbitig electro emits eergy whe it jumps from a outer orbit (higher eergy states) to a ier orbit (lower eergy states) ad also absorbs eergy whe it jumps from a ier orbit to a outer orbit. m h,m where, Outer eergy state m Ier eergy state,m Frequecy of radiatio The eergy absorbed or released is always i the form of electromagetic radiatios. ucleus MTHM TICL LYSIS OF BOHR' S THORY From above equatio (i) ad (ii) i.e., We get the followig results. Ze e mv 4 r r ad mvr h...(ii). Velocity of electro i th orbit : By puttig the value of mvr i equatio (i) from (ii) we get h Ze v 4 Z e Z v v h...(iii) 9.6 Where, v ms c m/s OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 where c 3 8 m/s speed of light i vacuum. Radius of the th orbit : From equatio (iii), puttig the value of v i equatio (ii), we get Z e h m r h r where r h r...(iv) Z me Z m.53å

4 J-Physics 3. Total eergy of electro i th orbit : From equatio (i) K Ze Zee mv ad 8 r P 4 r K.. P K Total eergy of the system K + P K + K K Ze 8 r By puttig the value of r from the equatio (iv), we get 4 Z me Z 8 h...(v) where ev 4. Time period of revolutio of electro i th orbit : r T v By puttig the values of r ad v, from (iii) ad (iv) h T T 4 Z me Z where, T secod 5. Frequecy of revolutio i th orbit : 4 Z me Z f f T 4 h where, f Hz 6. Wavelegt h of photo me Z 3.6 Z hc me Z h 8h c R R H R Z Rydberg costat where, is called wave umber m.97 3 Å (for statioary ucleus). If ucleus is ot statioary (i.e., mass of ucleus is ot much greater tha the mass of the revolvig particle like electro), the R R m / M where, m mass of revolvig particle ad M mass of ucleus 4 OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

5 J-Physics SPCTRL SRIS OF HYDROG TOM It has bee show that the eergy of the outer orbit is greater tha the eergy of the ier oes. Whe the Hydroge atom is subjected to exteral eergy, the electro jumps from lower eergy state i.e. the hydroge atom is excited. The excited state is ustable hece the electro retur to its groud state i about 8 sec. The excess of eergy is ow radiated i the form of radiatios of differet wavelegth. The differet wavelegth costitute spectral series. Which are characteristic of atom emittig, the the wave legth of differet members of series ca be foud from the followig relatios R This relatio explais the complete spectrum of hydroge. detailed accout of the importat radiatios are listed below. Lyma Series : The series cosist of wavelegth which are emitted whe electro jumps from a outer orbits to the first orbit i. e., the electroic jumps to K orbit give rise to lyma series. Here &, 3, 4,... The wavelegths of differet members of Lyma series are : 3R First member : I this case ad hece R 4 4 3R m 6Å OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 8R Secod member : I this case ad 3 hece R m 6Å 6 8R 8.97 Similarly the wavelegth of the other members ca be calculated. Limitig members : I this case ad, hece R R 9 m 9Å 6 R.97 This series lies i ultraviolet regio. Balmer Series : This series is cosist of all wave legths which are emitted whe a electro jumps from a outer orbit to the secod orbit i. e., the electro jumps to L orbit give rise to Balmer series. Here ad 3, 4, 5... The wavelegth of differet members of Balmer series. 5R First member : I this case ad 3, hece R R m 6563Å R Secod member : I this case ad 4, hece R R m 486Å R Limitig members: I this case ad, hece R 4 This series lies i visible ad ear ultraviolet regio Å R

6 J-Physics Pasche Series : This series cosist of all wavelegth are emitted whe a electro jumps from a outer orbit to the third orbit i. e., the electro jumps to M orbit give rise to pasche series. Here 3 & 4, 5, 6... The differet wavelegths of this series ca be obtaied from the formula R 3 where 4, 5, 6... For the first member, the wavelegths is 875Å. This series lies i ifra red regio. Bracket Series : This series is cosist of all wavelegths which are emitted whe a electro jumps from a outer orbits to the fourth orbit i. e., the electro jumps to orbit give rise to Brackett series. Here 4 & 5, 6, 7,... The differet wavelegths of this series ca be obtaied from the formula R 4 where 5, 6, 7... This series lies i ifra red regio of spectrum. Pfud series : The series cosist of all wavelegths which are emitted whe a electro jumps from a outer orbit to the fifth orbit i. e., the electro jumps to O orbit give right to Pfud series. Here 5 ad 6, 7, 8... The differet wavelegths of this series ca be obtaied from the formula R 5 where 6, 7, 8... This series lies i ifra red regio of spectrum. S. o. The result are tabulated below Series Ob s erved Valu e of Valu e of Positio i the S pectru m. Lyma Series,3,4... Ultra Violet. Balmer Series 3,4,5... Visible 3. Pasche Series 3 4,5,6... Ifra red 4. Brackett Series 4 5,6,7... Ifra red 5. Pfud Series 5 6,7,8... Ifra red Cotiuum th 5 excited state th 4 excited state rd 3 excited state d excited state st excited state Groud state Pfud Series Brackett Series Pasche Series Balmer Series Lyma Series 6.38 ev.54 ev.85 ev.5 ev 3.4 ev 3.6 ev OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

7 J-Physics XCITTIO D IOISTIO OF TOMS Cosider the case of simplest atom i. e., hydroge atom, this has oe electro i the iermost orbit i.e., ( ) ad is said to be i the uexcited or ormal state. If by some meas, sufficiet eergy is supplied to the electro. It moves to higher eergy states. Whe the atom is i a state of a high eergy it is said to be excited. The process of raisig or trasferrig the electro from lower eergy state is called excitatio. Whe by the process of excitatio, the electro is completely removed from the atom. The atom is said to be ioized. ow the atom has left with a positive charge. Thus the process of raisig the atom from the ormal state to the ioized state is called ioisatio. The process of excitatio ad ioisatio both are absorptio pheomea. The excited state is ot statioary state ad lasts i a very short iterval of time ( 8 sec) because the electro uder the attractive force of the ucleus jumps to the lower permitted orbit. This is accompaied by the emissio of radiatio accordig to BOHR'S frequecy coditio. photo of wavelegth photo of wavelegth + Ze + Ze spectrum origi of emissio spectra spectrum origi of absorptio spectra The eergy ecessary to excite a atom ca be supplied i a umber of ways. The most commoly kietic eergy (Wholly or partly) of the electros is trasferred to the atom. The atom is ow i a excited state. The miimum potetial V required to accelerate the bombardig electros to cause excitatio from the groud state is called the resoace potetial. The various values of potetial to cause excitatio of higher state called excitatio potetial. The potetial ecessary to accelerate the bombardig electros to cause ioisatio is called the ioizatio potetial. The term critical potetial is used to iclude the resoace, excitatio ad ioisatio potetial. We have see that the eergy required to excite the electro from first to secod state is ev from first to third state is ev., ad so o. The eergy required to ioise hydroge atom is ( 3.6) 3.6 ev. Hece ioizatio potetial of hydroge atom is 3.6 volt. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 SUCCSSS D LIMITTIOS Bohr showed that Plack's quatum ideas were a ecessary elemet of the atomic theory. He itroduced the idea of quatized eergy levels ad explaied the emissio or absorptio of radiatios as beig due to the trasitio of a electro from oe level to aother. s a model for eve multielectro atoms, the Bohr picture is still useful. It leads to a good, simple, ratioal orderig of the electros i larger atoms ad quatitatively helps to predict a greater deal about chemical behavior ad spectral detail. Bohr's theory is uable to explai the followig facts : The spectral lies of hydroge atom are ot sigle lies but each oe is a collectio of several closely spaced lies. The structure of multielectro atoms is ot explaied. o explaatio for usig the priciples of quatizatio of agular mometum. o explaatio for Zeema effect. If a substace which gives a lie emissio spectrum is placed i a magetic field, the lies of the spectrum get splitted up ito a umber of closely spaced lies. This pheomeo is kow as Zeema effect. 7

8 J-Physics x am ple hydroge like atom of atomic umber Z is i a excited state of quatum umber. It ca emit a maximum eergy photo of 4 ev. If it makes a trasitio to quatum state, a photo of eergy 4.8 ev is emitted. Fid, Z ad the groud state eergy (i ev) for this atom. lso, calculate the miimum eergy (i ev) that ca be emitted by this atom durig de excitatio. Groud state eergy of hydroge atom is 3.6 ev. Solu tio The eergy released durig de excitatio i hydroge like atoms is give by : 4 me Z 8h ergy released i de excitatio will be maximum if trasitio takes place from th eergy level to groud state i.e., 3.6 Z 4 ev...(i) & also 3.6 Z 4.8 ev...(ii) Takig ratio of (i) to (ii), we will get Puttig i equatio (i) we get Z Z4 3.6 Z ev groud state eergy is miimum if trasitio will be from to i.e. betwee last two adjacet eergy levels. mi ev is the miimum amout of eergy released durig de excitatio. x am ple sigle electro orbits aroud a statioary ucleus of charge +Ze where Z is a costat ad e is the magitude of electroic charge. It requires 47. ev to excite the electro from the secod orbit to third orbit. Fid (i) The value of Z. (ii) The eergy required to excite the electro from the third to the fourth Bohr orbit. (iii) The wavelegth of electroic radiatio required to remove the electro from first Bohr orbit to ifiity. (iv) Fid the K.., P.. ad agular mometum of electro i the st Bohr orbit. [ The ioizatio eergy of hydroge atom 3.6 ev, Bohr radius 5.3 m, Velocity of light 3 8 m/s, Plack's costat J s ] Solu tio The eergy required to excite the electro from to orbit revolvig aroud the ucleus with charge +Ze is 4 me give by Z 8h Z 3.6 (i) Sice 47. ev eergy is required to excite the electro from to 3 orbit 8 OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

9 J-Physics (ii) Z Z Z The eergy required to excite the electro from 3 to 4 is give by Z ev 44 (iii) The eergy required to remove the electro from the first Bohr orbit to ifiity is give by Z 3.6 5eV 34eV I order to calculate the wavelegth of radiatio, we use Bohr's frequecy relatio 34 8 hc hf (.6 9 )J Å (iv) K.. Ze mv J P.. K J 4 g r gular mometum mv r h.5 34 Js The radius r of the first Bohr orbit is give by r h.53 me Z 5 h.53 m.6 m.6 Å me x am ple isolated hydroge atom emits a photo of. ev. (i) Determie the mometum of photo emitted (ii) Calculate the recoil mometum of the atom (iii) Fid the kietic eergy of the recoil atom [Mass of proto m p.67 7 kg] Solu tio OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65..6 (i) Mometum of the photo is p 8 c kg m/s (ii) pplyig the mometum coservatio p p kg m/s p atom Photo p (iii) K mv (v recoil speed of atom, m mass of hydroge atom) K m p m p m Substitutig the value of the mometum of atom, we get K J

10 J-Physics Physical quatity F o r m u l a Ratio Formulae of hydroge atom Radius of Bohr orbit (r ) r h ; r 4 mkze.53 Z Å r : r :r 3...r :4:9... Velocity of electro i th Bohr v kze h ; v. 6 Z v :v :v 3...v : :... 3 orbit (v ) mke z Mometum of electro (p ) p ; p h Z p : p : p 3... p : : k Z mc gular velocity of electro( ) 3 3 h 3 4 ; Z 3 : : 3... : : h Time Period of electro (T ) T 4 k Z me 4 ; T 3 Z T :T :T 3...T :8:7:... : 3 Frequecy (f ) f Orbital curret (I ) I 4 4 k Z e m h k Z me 3 3 h 5 Z ; f Z ; I 3 3 f : f : f 3... f : 8 : I : I : I 3... I : 8 : gular mometum (J ) J h ; J J :J :J 3...J : : k Z me Cetripetal acceleratio (a ) a 4 4 h Z ; a 3 4 a : a : a 3... a : 6 : Kietic eergy ( k ) K RchZ Z ; K :... : 4 : 9... K K K RchZ Potetial eergy (U ) U Z ; U U : U : U 3...U : 4 : 9... Total eergy ( ) RchZ Z ; : : 3... : 4 : 9... OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

11 J-Physics X RYS ROTG XPRIMT Roetge discovered X ray. While performig experimet o electric discharge tube Roetge observed that whe pressure iside the tube is 3 mm of Hg ad applied potetial is kept 5 kv the some ukow radiatio are emitted by aode. These are kow as X ray. X rays are produced by bombardig high speed electros o a target of high atomic weight ad high meltig poit. evacuated tube + electro target cathode V X-rays To Produce X ray T hree T hi gs are Required (i) Source of electro (ii) Meas of acceleratig these electro to high speed (iii) Target o which these high speed electro strike COOLIDG MTHOD Coolidge developed thermoioic vacuum X ray tube i which electro are produced by thermoioic emissio method. Due to high potetial differece electros (emitted due to thermoioic method) move towards the target ad strike from the atom of target due to which X ray are produced. xperimetally it is observed that oly % or % kietic eergy of electro beam is used to produce X ray. Rest of eergy is wasted i form of heat. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 C h a r a c t e r i s t i c s o f t a r g e t F filamet C e e V(i kv) W widow T X-ray aode target (a) Must have high atomic umber to produce hard X rays. (b) High meltig poit to withstad high temperature produced. (c) High thermal coductivity to remove the heat produced water (d) Tatalum, plat i um, molybdeum a d tugste ser ve as target materials Cotrol of itesity : The itesity of X ray depeds o umber of electros strikig the target ad umber of electro deped o temperature of filamet which ca be cotrolled by filamet curret. Thus itesity of X ray depeds o curret flowig through filamet.

12 J-Physics Cotrol of Peetratig Power: The Peetratig power of X ray depeds o the eergy of icidet electro. The eergy of electro ca be cotrolled by applied potetial differece. Thus peetratig power of X ray deped o applied potetial differece. Thus the itesity of X ray depeds o curret flowig through filamet while peetratig power depeds o applied potetial differece Soft X ray Hard X ray Wavelegth Å to Å. Å Å ergy 4 ev Å 4 ev Å Peetratig power Less More Use Radio photography Radio therapy Cotiuous spectrum of X ray : Whe high speed electro collides from the atom of target ad passes close to the ucleus. There is coulomb attractive force due to this electro is deaccelerated i.e. eergy is decreased. The loss of eergy durig deacceleratio is emitted i the form of X rays. X ray produced i this way are called Brakig or Bremstralug radiatio ad form cotiuous spectrum. I cotiuous spectrum of X ray all the wavelegth of X ray are preset but below a miimum value of wavelegth there is o X ray. It is called cut off or threshold or miimum wavelegth of X ray. The miimum wavelegth depeds o applied potetial. e mv v K L M + e v h X-ray photo mv Loss i Kietic ergy mv mv h + heat eergy if v, v v (I first collisio, heat ) I mv h max...(i) V 3 V V mv ev...(ii) [here V is applied potetial] V > V > V 3 hc from (i) ad (ii) h max ev mi ev mi 4 V volt 4 V m volt Cotiuous X rays also kow as white X ray. Miimum wavelegth of these spectrum oly depeds o applied potetial ad does' t deped o atomic umber. Characteristic Spectrum of X ray Whe the target of X ray tube is collide by eergetic electro it emits two type of X ray radiatio. Oe of them has a cotiuous spectrum whose wavelegth deped o applied potetial while other cosists of spectral lies whose wavelegth deped o ature of target. The radiatio formig the lie spectrum is called characteristic X rays. Whe highly accelerated electro strikes with the atom of target the it kockout the electro of orbit, due to this a vacacy is created. To fill this vacacy electro jumps from higher eergy level ad electromagetic radiatio are emitted which form characteristic spectrum of X ray. Whose wavelegth depeds o ature of target ad ot o applied potetial. e K L M + e X-ray photo h e OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

13 From Bohr Model,, 3, 4...K series O J-Physics 4 series, 3, 4, 5...L series M M M M M series 3 3, 4, 5, 6...M series L L L L L series First lie of series Secod lie of series K K K K K K series Third lie of series Tr a sit io W a v e e r g y e r g y W a v e l e g t h l e g t h d i f f e r e c e L K K h K ( K L ) K hc ( ) K L 3 K 4 ( ) h K ( ) M K K h K ( K M ) K (3 ) h K K K K L evå hc ( ) 4 ( ) M M evå Relative itesity Bremsstrahlug cotiuum K Characteristic X-ray X-ray from a molybdeum target at 35 kv L L M L L h L ( L M ) L hc ( ) L M wavelegth (m) (3 ) h L 4 ( ) L M evå OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 MOSLY' S LW Moseley studied the characteristic spectrum of umber of may elemets ad observed that the square root of the frequecy of a K lie is closely proportioal to atomic umber of the elemet. This is called Moseley's law. Z atomic umber of target frequecy of characteristic spectrum (Z b) (Z b) a (Z b)...(i) b screeig costat (for K series b, L series b7.4) a proportioality costat From Bohr Model RcZ...(ii) Comparig (i) ad (ii) a Rc 3 Z K K

14 J-Physics Thus proportioality costat 'a' does ot deped o the ature of target but deped o trasitio. Bohr model Moseley' s correctio. For sigle electro species. For may electro species. 3.6Z ev. 3.6 (Z ) ev 3. RcZ 3. Rc(Z ) 4. RZ 4. R (Z ) For X ray productio, Moseley formulae are used because heavy metal are used. Whe target is same Whe trasitio is same (Z b) BSORPTIO OF X R Y Whe X ray passes through x thickess the its itesity I I e x I Itesity of icidet X ray I Itesity of X ray after passig through x distace absorptio coefficiet of material I Itesity of X ray decrease expoetially. I Maximum absorptio of X ray Lead Miimum absorptio of X ray ir x x am ple S o l u t i o Half thickess (x / ) The distace travelled by X ray whe itesity become half the origial value x / Whe X rays of wavelegth.5å pass through mm thick l sheet the their itesity is reduced to oe sixth. Fid the absorptio coefficiet for lumiium..33 I x I o log log 6.75 / mm 4 OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

15 J-Physics DIFFR CTIO OF X R Y Diffractio of X ray is possible by crystals because the iteratomic spacig i a crystal lattice is order of wavelegth of X rays it was first verified by Lauve. Diffractio of X ray take place accordig to Bragg's law d si d spacig of crystal plae or lattice costat or distace betwee adjacet atomic plae Bragg's agle or glacig agle Diffractig agle,, 3... d For Maximum Wavelegth si, max d so if > d diffractio is ot possible i.e. solutio of Bragg's equatio is ot possible. PROPRTIS OF X R Y X ray always travel with the velocity of light i straight lie because X rays are em waves X ray is electromagetic radiatio it show particle ad wave both ature I reflectio, diffractio, iterferece, refractio X ray shows wave ature while i photoelectric effect it shows particle ature. There is o charge o X ray thus these are ot deflected by electric field ad magetic field. X ray are ivisible. X ray affects the photographic plate Whe X ray icidets o the surface of substace it exerts force ad pressure ad trasfer eergy ad mometum Characteristic X ray ca ot obtaied from hydroge because the differece of eergy level i hydroge is very small. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 x am ple Show that the frequecy of K X ray of a material is equal to the sum of frequecies of K ad L X rays of the same material. Solu tio The eergy level diagram of a atom with oe electro kocked out is show above. ergy of ad of ad of thus L K K X ray is K L K K X ray is K M K L X rays is L M L K K + L or K K + L 5 K M L K

16 J-Physics PHOTOLCTRIC FFCT PHOTO LCTRIC FFCT It was discovered by Hertz i 887. He foud that whe the egative plate of a electric discharge tube was illumiated with ultraviolet light, the electric discharge took place more readily. Further experimets carried out by Hallwachs cofirmed that certai egatively charged particles are emitted, whe a Z plate is illumiated with ultraviolet light. These particles were idetified as electros. The pheomeo of emissio of electros from the surface of certai substaces, whe suitable radiatios of certai frequecy or wavelegth are icidet upo it is called photoelectric effect. XPL TIO OF PHOTOLCTRIC FFCT O the basis of wave theory :ccordig to wave theory, light is a electromagetic radiatio cosistig of oscillatig electric field vectors ad magetic field vectors. Whe electromagetic radiatios are icidet o a metal surface, the free electros [free electros meas the electros which are loosely boud ad free to move iside the metal] absorb eergy from the radiatio. This occurs by the oscillatios of electro uder the actio of electric field vector of electromagetic radiatio. Whe a electro acquires sufficietly high eergy so that it ca overcome its bidig eergy, it comes out from the metal. O the basis of photo theory: ccordig to photo theory of light, light cosists of particles (called photos). ach particle carries a certai amout of eergy with it. This eergy is give by h, where h is the Plak's costat ad is the frequecy. Whe the photos are icidet o a metal surface, they collide with electros. I some of the collisios, a photo is absorbed by a electro. Thus a electro gets eergy h. If this eergy is greater tha the bidig eergy of the electro, it comes out of the metal surface. The extra eergy give to the electro becomes its kietic eergy. XPRIM T S Hertz xperimet : Hertz observed that whe ultraviolet rays are icidet o egative plate of electric discharge tube the coductio takes place easily i the tube. ultraviolet rays cathode aode vacuated quartz tube Hallwach experimet : Hallwach observed that if egatively charged Z plate is illumiated by U.V. light, its egative charge decreases ad it becomes eutral ad after some time it gais positive charge. It meas i the effect of light, some egative charged particles are emitted from the metal. Leard xplaatio : He told that whe ultraviolet rays are icidet o cathode, electros are ejected. These electros are attracted by aode ad circuit is completed due to flow of electros ad curret flows. Whe U.V. rays icidet o aode, electros are ejected but curret does ot flow. For the photo electric effect the light of short wavelegth (or high frequecy) is more effective tha the light of log wavelegth (or low frequecy) 6 OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

17 J-Physics xperimetal study of photoelectric ffect : Whe light of frequecy ad itesity I falls o the cathode, electros are emitted from it. The electros are collected by the aode ad a curret flows i the circuit. This curret is called photoelectric curret. This experimet is used to study the variatio of photoelectric curret with differet factors like itesity, frequecy ad the potetial differece betwee the aode ad cathode. Light of itesity I ad frequecy Photoelectros Cathode (Photosesitive metal) ode i (Photoelectric curret) V Potetial Divider ( i ) Variatio of photoelectric curret with potetial differece : With the help of the above experimetal setup, a graph is obtaied betwee curret ad potetial differece. The potetial differece is varied with the help of a potetial divider. The graph obtaied is show below. i -V O ode Potetial V OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 The mai poits of observatio are : (a) (b) (c) (d) t zero aode potetial, a curret exists. It meas that electros are emitted from cathode with some kietic eergy. s aode potetial is icreased, curret icreases. This implies that differet electros are emitted with differet kietic eergies. fter a certai aode potetial, curret acquires a costat value called saturatio curret. Curret acquires a saturatio value because the umber of electros emitted 7 per secod from the cathode are fixed. t a certai egative potetial, the photoelectric curret becomes zero. This is called stoppig potetial (V ). Stoppig potetial is a measure of maximum kietic eergy of the emitted electros. Let K max be the maximum kietic eergy of a emitted electro, the K max ev. (ii) Variatio of curret with itesity The photoelectric curret is foud to be directly proportioal to itesity of icidet radiatio. ( i i i) ffect of itesity o saturatio curret ad stoppig potetial (a) Saturatio curret icreases with icrease i itesity. (b) Stoppig potetial (ad therefore maximum kietic eergy) is idepedet of itesity. 7 V i i ode Potetial V Itesity I ( I > I ) I

18 J-Physics ( i v) ffect of frequecy V (stoppig potetial) (a) (b) Stoppig potetial is foud to vary with frequecy of icidet light liearly. Greater the frequecy of icidet light, greater the stoppig potetial. There exists a certai miimum frequecy below which o stoppig potetial is required as o emissio of electros takes place. This frequecy is called threshold frequecy. For photoelectric emissio to take place, >. GOLD KY POITS (frequecy) Photo electric effect is a istataeous process, as soo as light is icidet o the metal, photo electros are emitted. Stoppig potetial does ot deped o the distace betwee cathode ad aode. The work fuctio represeted the eergy eeded to remove the least tightly bouded electros from the surface. It depeds oly o ature of the metal ad idepedet of ay other factors. Failure of wave theory of light (i) (ii) (iii) ccordig to wave theory whe light icidet o a surface, eergy is distributed cotiuously over the surface. So that electro has to wait to gai sufficiet eergy to come out. But i experimet there is o time lag. missio of electros takes place i less tha 9 s. This meas, electro does ot absorb eergy. They get all the eergy oce. Whe itesity is icreased, more eergetic electros should be emitted. So that stoppig potetial should be itesity depedet. But it is ot observed. ccordig to wave theory, if itesity is sufficiet the, at each frequecy, electro emissio is possible. It meas there should ot be existece of threshold frequecy. istei' s xplaatio of Photoelectric ffect istei explaied photoelectric effect o the basis of photo electro iteractio. The eergy trasfer takes place due to collisios betwee a electros ad a photo. The electros withi the target material are held there by electric force. The electro eeds a certai miimum eergy to escape from this pull. This miimum eergy is the property of target material ad it is called the work fuctio. Whe a photo of eergy h collides with ad trasfers its eergy to a electro, ad this eergy is greater tha the work fuctio, the electro ca escape through the surface. istei's Photoelectric quatio h K max Here h is the eergy trasferred to the electro. Out of this, is the eergy eeded to escape. The remaiig eergy appears as kietic eergy of the electro. ow K max ev (where V is stoppig potetial) h h + ev V e e Thus, the stoppig potetial varies liearly with the frequecy of icidet radiatio. Slope of the graph obtaied is h. This graph helps i determiatio of Plack's costat. e 8 V slope h e OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

19 J-Physics GOLD KY POITS istei's Photo lectric equatio is based o coservatio of eergy. istei explaied P... o the basis of quatum theory, for which he was awarded oble prize. ccordig to istei oe photo ca eject oe e oly. But here the eergy of icidet photo should greater or equal to work fuctio. I photoelectric effect all photoelectros do ot have same kietic eergy. Their K rage from zero to max which depeds o frequecy of icidet radiatio ad ature of cathode. The photo electric effect takes place oly whe photos strike boud electros because for free electros eergy ad mometum coservatios do ot hold together. x am ple Calculate the possible velocity of a photoelectro if the work fuctio of the target material is.4 ev ad wavelegth of light is m. What retardig potetial is ecessary to stop the emissio of electros? Solu tio s K max h mv hc max h v max hc m m/s The speed of a photoelectro ca be ay value betwee ad m/s If V is the stoppig potetial, the ev mvmax V mv max hc 4 e e e V hc 4 V m e OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 x am ple Solu tio The surface of a metal of work fuctio is illumiated by light whose electric field compoet varies with time as [ + cos t] si t. Fid the maximum kietic eergy of photoelectros emitted from the surface. The give electric field compoet is si t + si t cos t si t + The give light comprises three differet frequecies viz., + The maximum kietic eergy will be due to most eergetic photo. K max h h or 9 [ si ( + ) t + si( )t]

20 J-Physics x am ple Solu tio Whe light of wavelegth is icidet o a metal surface, stoppig potetial is foud to be x. Whe light of wavelegth is icidet o the same metal surface, stoppig potetial is foud to be wavelegth of the metal. x. Fid the threshold Let is the threshold wavelegth. The work fuctio is hc. ow, by photoelectric equatio ex hc hc...(i) ex hc hc...(ii) hc hc hc hc From (i) ad (ii) hc hc PHOTO THORY OF LIGHT photo is a particle of light movig with speed m/s i vacuum. The speed of a photo is idepedet of frame of referece. This is the basic postulate of theory of relativity. The rest mass of a photo is zero. i.e. photos do ot exist at rest. ffective mass of photo m c hc c h c i.e. m So mass of violet light photo is greater tha the mass of red light photo. ( R > V ) ccordig to Plack the eergy of a photo is directly proportioal to the frequecy of the radiatio. or h hc joule ( c ) or hc e Here eergy of photo, h J s, 4 ev Å hc 4( ev ) e c speed of light, h Plack's costat, e charge of electro frequecy of photo, wavelegth of photo Liear mometum of photo p h h c c photo ca collide with material particles like electro. Durig these collisios, the total eergy ad total mometum remai costat. ergy of light passig through per uit area per uit time is kow as itesity of light. Itesity of light P I t...(i) Here P power of source, rea, t time take eergy icidet i t time h Itesity I (h ) (h )...(ii) t From equatio (i) ad (ii), P (h ) umber of photo icidet i t time o. of photo per sec. t P h P 5 4 J hc m P Whe photos fall o a surface, they exert a force ad pressure o the surface. This pressure is called radiatio pressure. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

21 J-Physics Force exerted o perfectly reflectig surface Let '' photos are there i time t, Mometum before strikig the surface (p ) h Mometum after strikig the surface (p ) h Chage i mometum of photos p p h icidet photo h p h p reflected photo But chage i mometum of surface p h F h P P hc c F P I ad Pressure c c h h ; So that force o surface F t but P hc P I h Force exerted o perfectly absorbig surface p F p p t h h h t t ; F P c P hc ad Pressure F P I c c icidet photo o reflected photo p Whe a beam of light is icidet at agle o perfectly reflector surface x am ple F P c cos h cos I cos c F Pressure I cos c icidet photo reflected photo The itesity of sulight o the surface of earth is 4 W/m. ssumig the mea wavelegth of sulight to be 6 Å, calculate: (a) (b) Solu tio The photo flux arrivig at m area o earth perpedicular to light radiatios ad The umber of photos emitted from the su per secod (ssumig the average radius of arth's orbit to be.49 m) (a) ergy of a photo hc 4.6 ev J OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 x am ple Photo flux I photos/sec. (b) umber of photos emitted per secod P I 4 4 (.49 ) I a photoelectric setup, a poit source of light of power 3. 3 W emits moochromatic photos of eergy 5. ev. The source is located at a distace.8 m from the cetre of a statioary metallic sphere of work fuctio 3. ev ad radius 8 3 m. The efficiecy of photoelectro emissio is oe for every 6 icidet photos. ssumig that the sphere is isolated ad iitially eutral ad that photoelectros are istatly swept away after emissio, Fid (i) the umber of photoelectros emitted per secod. (ii) the time t after light source is switched o, at which photoelectro emissio stops.

22 J-Physics Solu tio ergy of a sigle photo 5. ev 8 9 J Power of source P 3. 3 W P 3. umber of photos emitted per secod 8 The umber of photos icidet per secod o metal surface is umber of electros emitted /s photo/s /s 4R r Source R.8m K max h ev The photoelectro emissio stops, whe the metallic sphere acquires stoppig potetial. r.8 3 m s K max. ev Stoppig potetial V V q 4 r q.78 C.78 ow charge q (umber of electros/secod) t e t s PHOTO CLL photo cell is a practical applicatio of the pheomeo of photo electric effect, with the help of photo cell light eergy is coverted ito electrical eergy. Costructio : photo cell cosists of a evacuated sealed glass tube cotaiig aode ad a cocave cathode of suitable emittig material such as Cesium (Cs). Workig: Whe light of frequecy greater tha the threshold frequecy of cathode material falls o the cathode, photoelectros emitted are collected by the aode ad a electric curret starts flowig i the exteral circuit. The curret icrease with the icrease i the itesity of light. The curret would stop, if the light does ot fall o the cathode. + aode m light pplicatio e e e e - e glass tube cathode key (i) I televisio camera. (ii) I automatic door (iii) Burglar s alarm (iv) utomatic switchig of street light ad traffic sigals. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

23 J-Physics DUL TUR OF LIGHT MTTR WVS THORY xperimetal pheomea of light reflectio, refractio, iterferece, diffractio are explaied oly o the basis of wave theory of light. These pheomea verify the wave ature of light. xperimetal pheomea of light photoelectric effect ad Crompto effect, pair productio ad positro ihalatioal ca be explaied oly o the basis of the particle ature of light. These pheomea verify the particle ature of light. It is iferred that light does ot have ay defiite ature, rather its ature depeds o its experimetal pheomeo. This is kow as the dual ature of light. The wave ature ad particle ature both ca ot be possible simultaeously. De- Broglie HYPOTHSIS De Broglie imagied that as light possess both wave ad particle ature, similarly matter must also posses both ature, particle as well as wave. De Broglie imagied that despite particle ature of matter, waves must also be associated with material particles. Wave associated with material particles, are defied as matter waves. De Brogli e wavelegth associ ated wi th movig parti cles If a particle of mass m movig with velocity v Kietic eergy of the particle associated with the particles is p m mv mometum of particle p mv m the wave legth h h h p mv m p v The order of magitude of wave legths associated with macroscopic particles is 4 Å. The smallest wavelegth whose measuremet is possible is that of rays ( 5 Å). This is the reaso why the wave ature of macroscopic particles is ot observable. The wavelegth of matter waves associated with the microscopic particles like electro, proto, eutro, particle, atom, molecule etc. is of the order of m, it is equal to the wavelegth of X rays, which is withi the limit of measuremet. Hece the wave ature of these particles is observable. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 De Brogli e wavelegth associ ated with the charged parti cles Let a charged particle havig charge q is accelerated by potetial differece V. Kietic eergy of this particle Mometum of particle p mv m mqv mv qv The De Broglie wavelegth associated with charged particle 3 h h h p m mqv For a lectro m e 9. 3 kg, q.6 9 C, h J s De Broglie wavelegth associated with electro.7 V meter.7 V Potetial differece required to stop a electro of wavelegth is V so V V 5.6 volt (Å)

24 J-Physics For Proto m p.67 x 7 kg De Broglie wavelegth associated with proto p V ; p.86 V meter.86 Å V For Deutero m d.67 7 kg, q d.6 9 C d V. V For Particles q.6 9 C, m kg V. V D BROGLI WVLGTH SSOCITD WITH UCHRGD PRTICLS p Kietic eergy of ucharged particle mv m m mass of particle, v velocity of particle, p mometum of particle. Velocity of ucharged particle v m Mometum of particle p mv m wavelegth associated with the particle Kietic eergy of the particle i terms of its wavelegth h h h p mv m h m h m.6 9 ev For a eutro m.67 7 kg meter ev.86 ev XPL TIO OF BOHR QUTIZTIO CODITIO ccordig to De Broglie electro revolves roud the ucleus i the form of statioary waves (i. e. wave packet) i the similar fashio as statioary waves i a vibratig strig. lectro ca stay i those circular orbits whose circumferece is a itegral multiple of De Broglie wavelegth associated with the electro, r h ad r mv h mvr This is the Bohr quatizatios coditio. equivalet straighteed orbit 4 6th Bohr orbit OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

25 x am ple Solu tio J-Physics Fid the iitial mometum of electro if the mometum of electro is chaged by p m ad the De Broglie wavelegth associated with it chages by.5 % d.5 d.5 ad p p m h p, differetiatig dp d h h p dp d p pm p p p m x am ple Solu tio particle moves i circular path of radius.83 cm i the presece of a magetic field of.5 Wb/m. Fid the De Broglie wavelegth associated with the particle. h p h qbr meter. Å mv r qvb x am ple Solu tio proto ad a particle are accelerated through same potetial differece. Fid the ratio of their de- Broglie wavelegth. h h h mv m mqv qv For proto m p m, q e For particle m 4 m, q e, p p p m q m q x am ple particle of mass m is cofied to a arrow tube of legth L. (a) Fid the wavelegths of the de Broglie wave which will resoate i the tube. (b) Calculate the correspodig particle mometa, ad (c) Calculate the correspodig eergies. Solu tio OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 (a) The de Broglie waves will resoate with a ode at each ed of the tube. Few of the possible resoace forms are as follows : (b) Sice de Broglie wavelegths are L( /) p h h,,,3... L (c) The kietic eergy of the particles are K 5 L,,,3... h p L3( /) p h,,, 3,... m 8L m L /

26 J-Physics TOMIC UCLUS UCLR PHYSICS The atomic ucleus cosists of two types of elemetary particles, viz. protos ad eutros. These particles are called ucleos. The proto (deoted by p) has a charge +e ad a mass m p kg, which is approximately 84 times larger tha the electro mass. The proto is the ucleus of the simplest atom with Z, viz the hydroge atom. The eutro (deoted by ) is a electrically eutral particle (its charge is zero). The eutro mass is kg. The fact that the mass of a eutro exceeds the mass of a proto by about.5 times the electroic masses is of essetial importace. It follows from this that the eutro i free state (outside the ucleus) is ustable (radioactive). With half life equal to mi, the eutro spotaeously trasforms ito a proto by emittig a electro (e ) ad a particle called the atieutrio. This process ca be schematically writte as follows : p + e + The most importat characteristics of the ucleus are the charge umber Z (coicidig with atomic umber of the elemet) ad mass umber. The charge umber Z is equal to the umber of protos i the ucleus, ad hece it determies the uclear charge equal to Ze. The mass umber is equal to the umber of ucleos i the ucleus (i.e., to the total umber of protos ad eutros). uclei are symbolically desigated as X Z or Z X where X stads for the symbol of a chemical elemet. 6 6 For example, the ucleus of the oxyge atom is symbolically writte as O 8 or 8O. The shape of ucleus is approximately spherical ad its radius is approximately related to the mass umber by R. /3 5 m. 5 /3 m Most of the chemical elemets have several types of atoms differig i the umber of eutros i their uclei. These varieties are called isotopes. For example carbo has three isotopes 6 C, 6 C 3, 6 C 4. I additio to stable isotopes, there also exist ustable (radioactive) isotopes. tomic masses are specified i terms of the atomic mass uit or uified mass uit (u). The mass of a eutral atom of the carbo 6 C is defied to be exactly u. u kg 93.5 MeV. BIDIG RGY The rest mass of the ucleus is smaller tha the sum of the rest masses of ucleos costitutig it. This is due to the fact that whe ucleos combie to form a ucleus, some eergy (bidig eergy) is liberated. The bidig eergy is equal to the work that must be doe to split the ucleus ito the particles costitutig it. The differece betwee the total mass of the ucleos ad mass of the ucleus is called the mass defect of the ucleus represeted by m [Zm p + ( Z)m ] m uc Multiplyig the mass defect by the square of the velocity of light, we ca fid the bidig eergy of the ucleus. B mc [(Zm p + ( Z)m ) m uc ]c If the masses are take i atomic mass uit, the bidig eergy is give by B [(Zm p + ( Z)m ) m uc ] 93.5 MeV Let us take example of oxyge ucleus. It cotais 8 protos ad 8 eutros. We ca discuss cocept of bidig eergy by followig diagram. 8 protos + 8 eutros 8m p + 8m > mass of ucleus of oxyge mass decreases releases eergy mass icreases absorbs eergy 6 ucleus of oxyge OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65

27 J-Physics B.. For ucleus we apply mass eergy coservatio, 8m p + 8m mass of ucleus + c For geeral ucleus Z X, mass defect differece betwee total mass of ucleos ad mass of the ucleus m [Zm p + ( Z)m ] M B.. mc (joules) (m) i amu 93.5 MeV Bidig ergy per ucleo Stability of a ucleus does ot deped upo bidig eergy of a ucleus but it depeds upo bidig eergy per ucleo B../ucleo B.. mass umber Stability B.. B../ucleo (MeV) 8.8MeV i Fe C He Li H (mass umber) (i) (ii) B../ is maximum for 6 (i), It is ±.3 MeV/ucleo, meas most stable uclei are i the regio of 6. Heavy uclei achieve stability by breakig ito two smaller uclei ad this reactio is called fissio reactio. small mass umbers large mass umber (iii) uclei achieve stability by combiig ad resultig ito heavy ucleus ad this reactio is called fusio reactio. small mass umbers large mass umber (iv) I both reactios products are more stable i compariso to reactats ad Q value is positive. OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65 UCLR COLLISIOS We ca represet a uclear collisio or reactio by the followig otatio, which meas X (a,b) Y a X Y + b (bombardig particle) (at rest) We ca apply : (i) Coservatio of mometum (ii) Coservatio of charge (iii) Coservatio of mass eergy For ay uclear reactio By mass eergy coservatio a X Y + b K K K K 3 4 (i) K + K + (m + m x )c K 3 + K 4 + (m Y + m b )c 7

28 J-Physics (ii) ergy released i ay uclear reactio or collisio is called Q value of the reactio (iii) Q (K 3 + K 4 ) (K + K ) K P K R (m R m P )c (iv) If Q is positive, eergy is released ad products are more stable i compariso to reactats. (v) If Q is egative, eergy is absorbed ad products are less stable i compariso to reactats. Q (B..) product (B..) reactats x am ple Let us fid the Q value of fusio reactio Q value for decay 4 He + 4 He 8 Be, if B.. B.. of He X ad Z X Z Y 4 + He 4 Q K + K Y...(i) Mometum coservatio, p Y p...(ii) of Be Y Q 8Y 8X K p m 4 p 4K m 4 4 K Y x am ple Solu tio 4K Q K K 4 4 K 4 Q For decay > which meas maximum part of released eergy is associated with K.. of. If Q is egative, the reactio is edoergic. The miimum amout of eergy that a bombardig particle must have i order to iitiate a edoergic reactio is called Threshold eergy th, give by th Q m m where m mass of the projectile. th miimum kietic eergy of the projectile to iitiate the uclear reactio m mass of the target How much eergy must a bombardig proto possess to cause the reactio 3 Li 7 + H 4 Be 7 + (Mass of 3 Li 7 atom is 7.6, mass of H atom is.783, mass of 4 Be 7 atom is 7.693) Sice the mass of a atom icludes the masses of the atomic electros, the appropriate umber of electro masses must be subtracted from the give values. Reactats : Total mass (7.6 3 m e ) + (.783 m ) m e e Products : Total mass ( m e ) m e The eergy is supplied as kietic eergy of the bombardig proto. The icidet proto must have more tha this eergy because the system must possess some kietic eergy eve after the reactio, so that mometum is coserved with mometum coservatio take ito accout, the miimum kietic eergy that the icidet particle must possess ca be foud with the formula. where, Q [( m e ) ( m e )] 93.5 MeV MeV th UCLR FISSIO m M Q 7 ( 63.96) 73. MeV I 938 by Hah ad Strassma. By attack of a particle splittig of a heavy ucleus ( > 3) ito two or more lighter uclei. I this process certai mass disappears which is obtaied i the form of eergy (eormous amout) + p excited ucleus B + C + Q 8 OD6\\Data\4\Kota\J-dvaced\SMP\Phy\Uit o-\moder Physics\g\_Moder Physics.p65