Introduction Learning Objectives On completion of tis capter you will be able to: 1. Define Compton Effect. 2. Derive te sift in incident ligt wavelengt and Compton wavelengt. 3. Explain ow te Compton wavelengt gets varied wit respect to various incident angles. 4. Discuss te experimental verification of Compton scattering. Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 1 of 7
COMPTON EFFECT:- Compton (1923) measured intensity of scattered X-rays from solid target, as function of wavelengt for different angles. He got Nobel prize for tat in 1927. Wen a beam of monocromatic radiation suc as X-rays, γ-ray, etc., of ig frequency is allowed to fall on a fine scatterer, te beam is scattered into two components namely one component aving te same frequency or wavelengt as tat of te incident radiation, so called unmodified radiation and te oter component aving lower frequency or iger wavelengt compared to incident radiation, so called modified radiation. te energy Let us consider te collision wic occurs between te poton (aving initially c ν = ) and electron. Te electron is free and is at rest before collision wit te incident poton. During collision, a part of energy is given to te electron, wic in turn increases te K.E. of te electron and ence it recoils at an angle of Φ as sown in figure. Te scattered poton moves wit an energy te original direction. c ν = ( < ν ) at an angle θ wit respect to Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 2 of 7
Obviously, one can use law of conservation of energy and momentum for suc a system. For tat, we ave to know te momentum and energy values before and after collision. Energy before collision Energy after collision c + mc c 2 2 e ' + were m is te mass of te electron at rest, m e is te mass of te scattering electron moving wit velocity v and c is te velocity of ligt. According to law of conservation of energy, Along x-axis, Momentum before collision c c + = ' + 2 2 e (1) Momentum after collision cos θ + m e v cos φ ' According to law of conservation of momentum, cos m e v cos = ' θ + φ (2) Similarly, on can write for y-axis, = sinθ mev sinφ (3) ' By solving te above tree equations*, one can get ' = (1 cos θ ) wic is te cange (or sift) in wavelengt. It is clear tat te wavelengt sift is independent of te wavelengt of te incident radiation as well as te nature of te scatterer and it is found to depend on te angle of scattering θ. * Te detailed derivation will be given at te class room session. Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 3 of 7
Case (i): Case (ii): Case (iii): Wen θ = o, ' = no scattering along te direction of incidence Wen θ = 9, ' = 6.6 *1 =.2445 A 9 *1 * 3 *1 34 =. 31 8 Tis difference in wavelengt is known as Compton wavelengt wen θ = 9. Wen θ = 18, 2 ' = =.4849 A. Hence, as θ varies from to 18, te wavelengt of te scattered radiation increases from to 2 +. Experimental verification: Consider te experimental set up sown in te following figure. Te monocromatic X-rays from a molybdenum target of an X-rays tube are made to fall on a carbon scatterer (grapite) and te corresponding values are calculated using Bragg s law. Te scattered X-ray is observed at te ionization camber or X-ray detector to to measure its intensity. Compton found tat te spectrum recorded after scattering ad K α line (corresponding to ) wic is on te longer wavelengt side of primary K α line (corresponding to ) as sown in figure. He also observed tat te cange in wavelengt increased rapidly as te scattering angle θ increased; te cange in wavelengt was independent of. Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 4 of 7
X-ray detector X-ray tube target (ligt atoms, e.g. grapite) e - A final word. We ve seen tat ligt can be described as a stream of particles called potons, but we don t ave to take tis picture too literally. Instead can tink of te situation as te electromagnetic wave excanging energy and momentum wit a carged particle in quantised amounts Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 5 of 7
Ceck Your Understanding (CYU) * 1. Define Compton effect. 2. A poton of energy E strikes a free electron, wit te scattered poton of energy E moving in te direction opposite tat of te incident poton. In tis Compton effect interaction, te resulting kinetic energy of te electron is (a) E, (b) E, (c) E E, (d) E + E, (e) none of te above. 3. An X-ray poton wit =6pm is scattered over 15 by a target electron. (i) Find te cange of its wavelengt. (ii) Find te angle between te directions of motion of te recoil electron and te incident poton. (iii) Find te energy of te recoil electron. Summary On completion of tis capter you ave learned te following: (1) Te classical wave teory of ligt cannot explain te scattering of x-rays from electrons. (2) Compton effect: Te decrease in energy (increase in wavelengt) of an x-ray or gamma ray poton wen interacting wit matter. (3) Te sifted in wavelengt is caused by te scattering of x-rays from free electrons and is given by ' = (1 cos θ ). (4) For a large energy transfer (and tus a measurable wavelengt sift), te poton energy sould be muc iger tan tat in te visible range X-rays. * (Ceck te correct answers on next page) Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 6 of 7
Activity On te basis of Compton Effect, it is apparent tat even toug ligt is a wave, it beaves like a particle. Can you guess? Is it possible to argue tis statement? If a wave beaves like a particle, in a reverse manner, is it possible for a particle (object) to exibit wave nature??? For example, as te bullet moving wit ig speed exibited wave nature or not? Just tink about it Suggested Reading 1. P.K. Palanisamy, Engineering Pysics, Scitec Publications Pvt Ltd, Cennai. 2. C. Santi et al., Engineering Pysics, Sonaversity, Salem. 3. M. Arumugam, Engineering Pysics, Anurada Agencies, Kumbakonam. (And some oter open resources from internet) Answers to CYU 1. Wen a beam of monocromatic radiation suc as X-rays, γ-ray, etc., of ig frequency is allowed to fall on a fine scatterer, te beam is scattered into two components namely one component aving te same frequency or wavelengt as tat of te incident radiation, so called unmodified radiation and te oter component aving lower frequency or iger wavelengt compared to incident radiation, so called modified radiation. 2. (c). Conservation of energy requires te kinetic energy given to te electron be equal to te difference between te energy of te incident poton and tat of te scattered poton. 3. (i) ' = 64.5 1 12 m (ii) ϕ = 14.4 (iii) 1.44keV Material prepared by: < Pysics Faculty > Topic No: < 2 > Page 7 of 7