Atomic and nuclear physics LEYBOLD Physics X-ray physics Leaflets P6.3.3.7 Physics of the atomic shell Compton effect: verifying the energy loss of the scattered x-ray quantum Objects of the experiment Measuring the transmission values and T2 of a Cu foil for unscattered x-rays and x-rays scattered at an aluminum body. Determining the wavelength shift for scattered x-rays from the change in the transmission. ■ I Comparing the measured wavelength shift with that calculated on the basis of the Compton scattering. Principles Compton effect: In 1923,the American physicist A.H.Compton observed a collision and1 and A2 are the wavelengths of the x-ray wavelength shift in x-rays scattered at a scattering body,which quantum before and after collision,a relativistic formulation of he explained on the basis of the quantum nature of x-rays.He the conservation of energy gives us interpreted this effect as a collision between an x-ray quantum and an electron of the scattering material,in which the energy h.c +mo.c2=h.c m0·c2 E=h.c A1 2 0 V1- h:Planck's constant mo:mass of electron c:velocity of light The momentum of an x-ray quantum is λ：wavelength of the x-ray quantum changes,as the kinetic energy is trans- h p= (0 ferred to the electron. In the collision,energy and momentum are conserved.Before The conservation of momentum is thus the collision,the electron can be considered as being at rest (see Fig.1).When v is the velocity of the electron after the hh mo 入1 入2 and Fig.1 Compton scattering of an x-ray quantum at an electron at mo 0= sin λ2 y.sin (. rest 1- collision angles (see Fig.1). We can apply some transformations to (l)and (IV)to arrive at the following relation for the change in the wavelength: A2-入1 mo·c1-cos8) h (M The quantity moc=2.43 pm h (VI) C is termed the Compton wavelength Ac.It is identical to the wavelength of a photon having an energy equal to the resting energy of the electron.Fig. 1 Compton scattering of an x-ray quantum at an electron at rest. Atomic and nuclear physics X-ray physics Physics of the atomic shell LEYBOLD Physics Leaflets Compton effect: verifying the energy loss of the scattered x-ray quantum Objects of the experiment Measuring the transmission values T1 and T2 of a Cu foil for unscattered x-rays and x-rays scattered at an aluminum body. Determining the wavelength shift for scattered x-rays from the change in the transmission. Comparing the measured wavelength shift with that calculated on the basis of the Compton scattering. Principles Compton effect: In 1923, the American physicist A. H. Compton observed a wavelength shift in x-rays scattered at a scattering body, which he explained on the basis of the quantum nature of x-rays. He interpreted this effect as a collision between an x-ray quantum and an electron of the scattering material, in which the energy E = h ⋅ c l (I) h: Planck’s constant c: velocity of light l: wavelength of the x-ray quantum changes, as the kinetic energy is trans￾ferred to the electron. In the collision, energy and momentum are conserved. Before the collision, the electron can be considered as being at rest (see Fig. 1). When v is the velocity of the electron after the collision and l1 and l2 are the wavelengths of the x-ray quantum before and after collision, a relativistic formulation of the conservation of energy gives us h ⋅ c l1 + m0 ⋅ c2 = h ⋅ c l2 + m0 ⋅ c2 √1 −    v c    2 (II) m0: mass of electron The momentum of an x-ray quantum is p = h l (III) The conservation of momentum is thus h l1 = h l2 ⋅ cos q + m0 √1 −    v c    2 ⋅ v ⋅ cos w and 0 = h l2 ⋅ sin q + m0 √ 1 −    v c    2 ⋅ v ⋅ sin w (IV). q, w: collision angles (see Fig. 1). We can apply some transformations to (II) and (IV) to arrive at the following relation for the change in the wavelength: l2 − l1 = h m0 ⋅ c (1 − cosq) (V) The quantity h m0 ⋅ c = 2.43 pm (VI) is termed the Compton wavelength lC. It is identical to the wavelength of a photon having an energy equal to the resting energy of the electron. P6.3.3.7 0508-Ste 1