12. A beam of 3-MeV photons with intensity 108 cm-2s-1 irradiates a small sample of water. (a) How many photon-water interactions occur in one second in one cm³ of the water? (b) How many positrons are produced per second in one cm3 of the water?

6. One form of nuclcar radiation, beta decay, occurs when a neutron changes into a proton, an clectron, and a neutral particle called an antineutrino: n → p+ + e¯ +Ve, where ve is the symbol for an antincutrino. When this change happens to a neutron within the nucleus of an atom, the proton remains behind in the nucleus while the clectron and neutrino are ejected from the nucleus. The ejected electron is called a beta particle. One nucleus that exhibits beta decay is the isotope of hydrogen ³H, called tritium, whose nucleus consists of one proton (making it hydrogen) and two neutrons (giving tritium an atomic mass m = 3u). Tritium is radioactive, and it decays to helium: 3H → *He + e¯+Ve• (a) Is charge conserved in the beta decay process? Explain. (b) Why is the final product a helium atom? Explain. (c) The nuclei of both 3H and 3He have radii of 1.5 x 10 15 speed must the electron be ejected if it is to escape from the nucleus and not fall back? m. With what minimum

d) Using the SEMF show that the neutron separation energy S, is given approximately by 1-2A + 4Z A 2as 3A¹/3 ac Z² + 3 A4/3 Snav You may use the approximations Z(Z − 1) ≈ Z², A(A − 1) ≈ A² and (A − 1)" ≈ An — nA¹-1, and ignore the pairing term. + as

25. Alpha particles are emitted in nuclear decay processes with typical energies of 5 MeV. In analogy with Example 4.9, determine the range of kinetic energies of an alpha particle trapped in a nucleus-sized region and deduce whether the alpha particle can exist inside the nucleus.