Download Nuclear radiations can be divided into three categories : 1. Charged particles like electr and more Schemes and Mind Maps Nuclear Physics in PDF only on Docsity! Photoelectric Effect A gamma ray can transfer its energy to an electron originally bound in an atom because the atom can then take up some of the recoil momentum, as shown in Fig. (3.3). Conservation of momentum ๐๐พ = ๐๐ + ๐๐ (3.20) and Conservation of energy ๐ธ๐พ = ๐๐ +๐๐ +๐ธ๐ต (3.21) Fig. 3.3: Interaction of a gamma ray with a bound electron . can be simultaneously satisfied. In Eq. (3.21), ๐ธ๐ต is the binding energy of the electron in the atom, which is also the excitation energy of the atom after the electron has been ejected. It is not difficult to show that the recoil kinetic energy ๐๐ is of order (๐0/๐0) ๐๐ , where ๐0 ๐๐๐ ๐0 are the masses of the electron and atom, respectively. Since ๐0/๐0 โ 10โ4, ๐๐ can be neglected for most purposes so that ๐๐ = โ๐ โ๐ธ๐ต (3.22) For gamma rays above about 1 2 ๐๐๐, photoelectrons are most probably ejected from the ๐พ ๐ โ๐๐๐ of an atom because, for these electrons, the classical resonance condition is most nearly satisfied. The photoelectric effect is always accompanied by a secondary process, since the atom does not remain in its excited energy state ๐ธ๐ต. Either ๐ฅ โrays are emitted by the atom, or electrons are released from the outer atomic shells, which carry away the available excitation energy. These are called Auger electrons. In any dense material, the secondary radiations are absorbed in turn with a high probability. This occurs in most scintillators which are used for gamma-ray detection . Example 3.8: A 3 โ ๐๐๐ photon interacts by Compton scattering. (๐) What is the energy of the photon and the electron if the scattering angle of the photon is 90ยฐ? (b) What is that energy if the angle of scattering is 180ยฐ? Solution: (๐) ๐ธ๐พ โฒ = ๐ธ๐พ 1+ 1โ๐๐๐ ๐ ๐ธ๐พ/๐๐2 ๐ธ๐พ โฒ = 3 1 + 1 โ 0 3/0.511 ๐ธ๐พ โฒ = 0.437 ๐๐๐ ๐๐ = ๐ธ๐พ โ ๐ธ๐พ โฒ ๐๐ = 3 โ 0.437 = 2.563 ๐๐๐ (๐) ๐ธ๐พ,๐๐๐ โฒ = ๐ธ๐พ 1 + 2๐ธ๐พ/๐๐2 = 3 1 + 2(3)/0.511 ๐ธ๐พ,๐๐๐ โฒ = 0.235 ๐๐๐ ๐๐ = 3 โ 0.235 = 2.765 ๐๐๐ Example 3.9: What is the minimum energy of the ๐พ โray after Compton scattering if the original photon energy is 0.511, 5, 10, or 100 ๐๐๐? Solution: ๐ธ๐พ,๐๐๐ โฒ = ๐ธ๐พ 1+2๐ธ๐พ/๐๐2 ๐๐๐๐๐ข๐ ๐ ๐ = 1800 for minimum energy of the ฮณ-ray after Compton scattering. The results are shown in the table below. PROBLEM 3.1 The gamma-ray photon collides with an electron at rest. It is scattered through 900, what is it frequency after collision, if itโs initial frequency is (3 ร 1019 ๐ป๐ง) ?
