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Quantum Mechanics https://www.youtube.com/watch?v=cz27jq4ATL4 Reference: Concepts of Modern Physics “A. Beiser” 1 Compton Effect In 1923, Compton while studying the scattering of X-rays by a block of graphite observed that two types of X- rays were found in scattered rays. One, whose wavelength is same as that of incident X-rays and other, whose wavelength is greater than that of incident X-rays. This difference in wavelength called Compton shift which depends on scattering angle and this effect is known as Compton Effect. Compton effect is the outcome of collision between the high energy photon and free e-. pp sin pe 0 pp pp cos pe cos h c after collision before collision pe sin •Loss in photon energy=gain in electron energy K h-h K •Since rest mass of photon is zero, E=pc again E=h , therefore, p=h /c. Now if we consider momentum conservation in the direction of original photon and in the direction perpendicular to it then we have h h 0 cos pcos ...(i) c c h 0 sin psin ...(ii) c h h 0 cos pcos ...(i) c c h 0 sin psin ...(ii) c pc cos h h cos pc sin h sin By squaring and adding we get p 2 c 2 (h ) 2 2h 2 cos (h ) 2 .......(iii ) total energy of Electron E K m0 c 2 m02c 4 p 2c 2 K m0 c 2 2 m02 c 4 p 2c 2 or , p 2 c 2 K 2 2m0 c 2 K Since K h h ' We have p c (h ) 2h 2 (h )2 2m0c 2 (h h ) .... (iv) 2 2 2 Equating equations iii and iv we obtain 2m0c 2 (h h ) 2h2 (1 cos ) .......(v) Dividing equation v by 2h 2c 2 we get m0 c (1 cos ) h c c c c m c 1 1 (1 cos ) or , 0 h Therefore, h (1 cos ) .........(vi ) m0 c Equation vi shows Compton shift. h c 0.0024nm or 2.4 pm is known as compton wavelength m0 c for scattering particle (electron). Note: Case I: when =0o , λ=0 Case II: when =90o , λ=λ c Case III : when 180o , 2c 4.8 pm Realtion between and pc sin h sin pc cos h h cos h sin 2sin( / 2)cos( / 2) h h cos / cos h (1 cos ) m0c 1 1 h (1 cos ) 2 m0c tan h (1 cos ) 1 let 2 m0c (1 cos ) 1 2sin( / 2)cos( / 2) tan (1 cos ) 1 cos 2sin( / 2)cos( / 2) tan ( 1)(1 cos ) 2sin( / 2)cos( / 2) tan ( 1)2sin 2 ( / 2) h m0c 2 cot / 2 tan h 1 m0 c 2 Compton effect • (h/m0c) is known as Compton wavelength of the scattering particle. For an electron it is 0.024 Å. • This phenomenon gives a very strong evidence in support of the quantum theory of radiation. • Observe the difference in wavelength for various values of . Quest: Q1: An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases, or (c) remains the same. Ans: (b) Q2. A photon of energy E0 strikes a free electron. The scattered photon with energy E moves in opposite direction that of the incident photon. In this Compton effect interaction, the resulting kinetic energy of the electron is (a) E0 , (b) E , (c) E0 E , (d) E0 + E , (e) none of the above. Ans: (c) Q3. Deduce the expression for the maximum kinetic energy of the recoiled electron. Q4. Why Compton effect not observed with visible light. Q5. Explain the presence of unmodified scattered radiation along with modified radiations for non zero scattering angle.