FACULTY OF SCIENCE, WINTER 2008

PHYS 126 LEC B3 : Fluids, Fields and Radiation (Instructor: Marc de Montigny)

Walker, Physics, Chapter 32: Nuclear Physics and Nuclear Radiation

• Section 32-1: The Constituents and Structure of Nuclei
  • P. 1072, Eq. 32-1: A = Z + N, where
    • A (mass number) is the number of nucleons (protons and neutrons) in the nucleus
    • Z (atomic number) is the number of protons in the nucleus
    • N (neutron number) is the number of neutrons in the nucleus
  • Walker (and many texts) use this notation for nuclei. On this page, I will use X(A,Z) instead. For instance, C(13,6) has 13 nucleons: 6 protons and 13 - 6 = 7 neutrons.
  • P. 1073 Table 32-2 contains the mass and charge of particles in the atom
  • Isotopes are nuclei with same Z but different N.
  • Elements are determined by Z.
  • Some units of mass/energy:
    • P. 1073, Eq. 32-2: Atomic Mass Unit 1 u = 1.660540 × 10^-27 kg
    • P. 1073, Eq. 32-3: 1 u = 931.5 MeV/c²
  • P. 1074, Eq. 32-4: r = (1.2 × 10^-15 m) A^1/3
  • P. 1074: 1 fermi = 1 fm = 10^-15 m
  • P. 1107 Problem 4
  • P. 1107 Problem 6
  • P. 1075: Nuclear Stability
    • Gravity is negligible at nuclear level.
    • Protons are repelled by electrostatic force. Neutrons are neutral.
    • Need for strong attractive forces in the nucleus: strong nuclear force.
    • The strong force is short range (distance of a couple fermis).
    • The strong force is attractive and acts with nearly equal strength between protons - protons, protons - neutrons, and neutrons - neutrons.
    • The strong force does not act on electrons.
  • P. 1076 Figure 32-1 shows N and Z for stable and unstable nuclei.
• Section 32-2: Radioactivity
  • Radioactivity occurs when unstable nuclei emit particles.
  • Here we consider three types of radioactive (or decay) processes:
    • alpha : X(A,Z) → X(A-4,Z-2) + He(4,2). Alpha particles are nothing but helium nuclei. P. 1078, Example 32-3 we find N = 144, Z = 90.
    • beta : X(A,Z) → Y(A,Z+1) + e^- (for negative beta emission) or X(A,Z) → Y(A,Z-1) + e⁺ (for positive beta emission). P. 1080, Example 32-4 we find N = 7, Z = 7, and A remains equal to 14.
    • gamma : gamma rays carry energy, and this type of decay result from the transition from an excited state to a lower state. For example, N*(14,7) → N(14,7) + γ.
• Section 32-3: Half-Life and Radioactive Dating
  • You may picture nuclear decay as a melting chunk of ice. The mass of ice decreases as a function of time. For nuclei, instead of mass, we measure the number of nuclei N (also referred to as sample size) or the activity, which is the decay rate ΔN/Δt.
  • Note: Do not confuse the sample size N with the neutron number!
  • It is found that the decay rate is proportional to the sample size: ΔN/Δt = (constant) × N.
  • We write ΔN/Δt = - λ N.
  • P. 1084, Eq. 32-9: N(t) = N₀ e^{-λ t}, where N₀ = N(t=0)
  • λ = decay constant
  • Unit of λ : s^-1
  • Meaning of λ : after a time t = λ^-1, N has been reduced to 37% (= e^-1) of its initial value. Therefore, the larger λ is, the faster the nuclei will decay.
  • P. 1085, Figure 32-6 displays the dependance on the decay constant λ.
  • P. 1085, the Half-life T_1/2 of a nucleus is the time required for the number of such nuclei to decrease by a factor 2.
  • N(T_1/2) = (1/2) N₀ = N₀ e^{-λ T_1/2} leads to
  • P. 1085, Eq. 32-10: T_1/2 = ln(2)/λ, where ln(2) ≈ 0.693
  • Activity, or decay rate R:
    • P. 1086, Eq. 32-11: R = |ΔN/Δt| = λ N
    • P. 1086, Eq. 32-12: R = λN₀ e^-λt = R₀ e^-λt
  • P. 1108 Problem 24
  • P. 1108 Problems 27 and 28
  • P. 1108 Problem 30
  • P. 1108 Problem 34
• Section 32-4: Nuclear Binding Energy
  • E = Δ m c² is the binding energy, i.e. the energy required to separate a nucleus into its individual nucleons.
  • Δ m = M_{all nucleons} - M_nucleus
• Section 32-5: Nuclear Fission [Omitted]
• Section 32-6: Nuclear Fusion [Omitted]
• Section 32-7: Practical Applications of Nuclear Physics
  • The section below describes biological effects of radiation.
  • P. 1095, Eq. 32-15, Roentgen : 1 R = 2.58 × 10^-4 C/kg, for X-rays or γ rays in dry air at standard temperature and pressure. [We will not use it hereafter.]
  • The absorbed dose of radiation is the amount of radiation energy absorbed per unit mass of tissue.
  • P. 1096, Eq. 32-16, Radiation Absorbed Dose : 1 rad = 0.01 J/kg for any type of radiation
  • P. 1096, Eq. 32-17, Relative Biological Effectiveness : RBE = (dose of 200-keV X-rays necessary to produce a given biological effect)/ (dose of a particular type of radiation necessary to produce the same biological effect). [Note that we will not use this definition; instead we will simply take the appropriate values of RBE and use them in Eq. 32-18, below.]
  • P. 1096, Table 32-3 shows the RBE for various types of radiation.
  • Biologically Equivalent Dose
    • It allows to measure the biological damage caused by exposure to radiation.
    • P. 1096, Eq. 32-18, Roentgen Equivalent in Man (rem): (dose in rem) = (dose in rad) × RBE.
    • P. 1097, Table 32-4 shows typical radiation dosages.
  • P. 1108 Problem 54
  • P. 1108 Problem 56
  • P. 1108 Problem 57
• Section 32-8: Elementary Particles [Omitted]
• Section 32-9: Unified Forces and Cosmology [Omitted]

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