国际物理林匹克竞赛试题ThQIVAtomicsSolution.docVIP

Atomics - Problem IV (7 points) Compton scattering A photon of wavelength is scattered by a moving, free electron. As a result the electron stops and the resulting photon of wavelength scattered at an angle with respect to the direction of the incident photon, is again scattered by a second free electron at rest. In this second scattering process a photon with wavelength of emerges at an angle with respect to the direction of the photon of wavelength. Find the de Broglie wavelength for the first electron before the interaction. The following constants are known: - Planck’s constant - mass oh the electron - speed of light in vacuum Problem III - Solution The purpose of the problem is to calculate the values of the speed, momentum and wavelength of the first electron. To characterize the photons the following notation are used: Table 4.1 initial photon photon – after the first scattering final photon momentum energy wavelength  To characterize the electrons one uses Table 4.2 first electron before collision first electron after collision second electron before collision Second electron after collision momentum energy speed The image in figure 4.1 presents the situation before the first scattering of photon. Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 To characterize the initial photon we will use his momentum and his energy ( 4.1) ( 4.2) is the frequency of initial photon. For initial, free electron in motion the momentum and the energy are ( 4.3) where is the rest mass of electron and is the mass of moving electron. As usual, . De Broglie wavelength of the first electron is The situation after the scattering of photon is described in the figure 4.2. To characterize the scattered photon we will use his momentum and his energy ( 4.4). where ( 4.5) is the frequency of scattered photon. The magnitude of momentum of the electron ( that r