Bremsstrahlung –”braking radiation” Consider essentially the reverse process of the photoelectric effect, the impact of high- energy electrons (KE~10 keV) on a surface (or another particle) Since the electrons rapidly decelerate, one expects the production of EM radiation Classically, the radiation frequency should cover the entire spectrum, i.e. all frequencies
Experimentally, a maximum frequency fmax (or minimum wavelength lmin ) is observed For very short wavelengths (l~0.01-10 Å), we need to treat EM radiation like a particle, i.e. photons So, consider the same conservation of energy relation as used for the photoelectric effect However, KE=10 keV>> f (the work function), so we can neglect f ®®®® KEbefore = hf + KEafter Maximum photon frequency occurs for KE =0 ®®® KEbefore after fmax = All electron KE is converted h to photon energy (x-ray) hc l = Further evidence of particle min KE behavior of EM radiation before Compton Scattering
Scattering of EM radiation (x-rays) off of a “free” electron Classically, if the radiation is treated as a wave one expects the following: - radiative “pressure” should slowly cause the electron to accelerate in the direction of the wave propagation - the electrons would absorb the radiation of frequency f and reradiate (scattering), but in all directions. However, a Doppler shift would slowly develop as the electron accelerated. The emitted frequency f’ would be shifted. ØSince the electron should absorb different amounts of energy (since it is accelerating, and the electron sees the EM wave slowly being redshifted), a broad distribution of Doppler-shifted frequencies was expected ØThis was not observed! ØIn 1932, Compton found that for a given detector angle q, only one frequency f’ (l’) was observed ®® ØAgain, the classical wave picture fails when considering EM radiation of very short wavelength ØThe quantum particle picture is then adopted to explain this effect as an elastic collision. Apply - conservation of energy - conservation of momentum! ØThe change in wavelength is found to be h l'-l = Dl = (1- cosq ) mec ØDl depends only on the scattered photon angle ØIndependent of time; contrary to classical expectations Øl’>l, since photon loses energy, electron gains KE ØWhen q=180°, Dl is maximum; called back scattering 2h Dlmax = mec ØCompton’s experiment was the first proof of the photon’s momentum ØAgain, the particle interpretation of radiation is required As mentioned, Compton scattering on an electron is an elastic process since the electron’s mass cannot change However, inelastic Compton scattering can occur on composite particles, i.e. a nucleus, whose mass (internal energy) can change. Conservation of total energy still holds. Inelastic Compton scattering is not relevant to atoms. It would involve the removal of an electron, but the electron binding energy (~10 eV, also called the ionization potential) is much less than the energy of an x-ray Finally, the predictions of classical wave theory are valid if the wavelength is large, or f small Pair Production For photon collisions we have seen that it is possible for the photon to give up all of its energy (photoelectric effect; visible or ultraviolet) or some of its energy (Compton effect; x-ray) If the photon is a gamma ray (g-ray; l <0.01 Å or E> 1 MeV), it can spontaneously give up all of its energy to produce a particle – antiparticle pair The process, however, cannot occur in a vacuum, but results from an electromagnetic interaction when the g-ray passes near an atomic nucleus Without the atomic nucleus, momentum conservation is violated. The extra particle is needed to remove extra momentum Bubble chamber with magnetic field pointing out of the figure
A general rule: all reactions require at least two reactants and two products so that momentum is conserved The heavier of the two particles will always have a smaller change in KE For pair production, the photon again must be treated as a particle!