ZX or X-A where X is chemical symbol of element. common unit: [unified mass unit = u] also known as [atomic mass unit = amu] or [Dalton = Da]
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1 1 Part 5: Nuclear Physics 5.1. The Nucleus = atomic number = number of protons N = neutron number = number of neutrons = mass number = + N Representations: X or X- where X is chemical symbol of element Examples: or C-12, Pu or Pu-239 C 6 93 Isotopes: same, different N and Examples: C 6 C 6 C 6 C Charge of Nucleus Q = e = (1.6x10-19 C) Mass of Nucleus common unit: [unified mass unit = u] also known as [atomic mass unit = amu] or [Dalton = Da] definition: mass of neutral, ground state C-12 atom = 12 u conversions: [1 u = x10-27 kg = MeV/c 2 ] Radius of Nucleus r = r 0 1/3 where r o = 1.2x10-15 m = 1.2 fm Strong Nuclear Force attractive force between nucleons (n-n, n-p, p-p) short-ranged very strong (must overcome p-p repulsion)
2 2 Binding Energy E b = m c 2 where mass deficit: m = m H 1 + ( )m n m atom Find the binding energy of a C-14 nucleus and the binding energy per nucleon. ns MeV and 7.52 MeV per nucleon 5.2 Radioactivity Types of Nuclear Radiation p n bound together (He-4 nucleus) electron positron (antielectron) gamma ray photon (sometimes emitted after or β decay from excited daughter) lpha Decay Big nucleus ejects alpha. Decay Equation: Energy released in decay: Q = m c Parent Daughter + He where mass deficit m = m parent m daughter m He 4 If gamma decay follows, part of this energy is the gamma ray photon energy with the remaining part going to kinetic energy of alpha. The gamma ray comes from the excited alpha daughter (indicated with the * in the decay equations) Parent Daughter + He 4 2Daughter 4 2Daughter + γ
3 3 (a) Write the alpha and gamma decay equations for Ra-226. (b) Find the total energy released in the decay. If the gamma ray emitted has a wavelength of nm, then how much kinetic energy is left for the alpha particle? ns. (a) 88Ra 86Rn He then 86Rn Rn + γ (b) Q = MeV with MeV of kinetic energy Beta-Minus Decay Inside the nucleus n p + + e + ν where e - is electron (β - ) and ν is antineutrino. Decay Equation: Energy released in decay: Q = m c 2 Parent Daughter + β + ν where mass deficit m = m parent m daughter If gamma decay follows, part of this energy is the gamma ray photon energy with the remaining part going to kinetic energy of beta. The gamma ray comes from the excited alpha daughter (indicated with the * in the decay equations). Parent Daughter + β + ν Daughter Daughter + γ Write the beta decay equation for C-14 and find the energy released in the decay ns. 6C 7 N + β + ν and Q = 0.16 MeV 1 0
4 4 Beta-Plus Decay Only occurs for neutron-deficient nuclei. Inside the nucleus p + + Energy n + e + + ν where e + is positron (β + ) and is neutrino. Decay Equation: Parent Daughter + β + ν 1 Write the beta decay equation for N ns. 7N 6 C β + ν +1 0 Electron Capture (EC) nother way for neutron-deficient nucleus to decay. n electron is captured by the nucleus from the inner shell of the atom and combines with a proton to form a neutron and neutrino. The neutrino is ejected. p + + e n + ν Population Decay N(t) = N o e λt N o = number of unstable nuclei at t = 0 [#] N(t) = number of unstable nuclei at time t [#] = decay constant [1/s]
5 5 Half-Life (T 1/2 ) t t = T 1/2, the population reduces by one-half. N(T 1/2 ) = N o / 2 T 1/2 = ln 2 λ = λ ctivity The rate of decay is the activity. R(t) = λ N(t) R(t) = R o e λt Units of activity: mks [decay/s = Becquerel = Bq] common [Curie = Ci] [1 Ci = 3.7x10 10 Bq] Probability of Decay The probability that nuclei will decay in the next unit of time t is P(t) = 1 e λt = 1 e 0.693/T 1/2
6 6 Health Effects exposure absorbed dose equivalent dose = absorbed dose RBE factor RBE (relative biological effectiveness) factor is a number that depends on type and energy of radiation. Typical values: gamma 1 beta 1-2 alpha Name Description mks unit common unit conversion Exposure amount of ionizing [C/kg] [Roentgen = R] [1 C/kg = 3876 R] radiation exposed to bsorbed Dose amount of ionizing radiation absorbed by tissues [Gray = Gy] [rad] [1 Gy = 100 rads] Equivalent Dose absorbed dose times RBE factor [Sievert = Sv] [rem] [1 Sv = 100 rems] The equivalent dose and the duration of the dose are the most important quantities in determining health risk. verage annual natural background level ~ 310 mrem (2/3 from thoron and radon, 1/3 from other terrestrial sources, cosmic rays, internal isotopes) verage annual artificial background level ~ 310 mrem (mainly from medical procedures) nnual recommended limits beyond background: 100 mrem general public, 5000 mrem occupational from U.S. Nuclear Regulatory Commission
7 7 5.3 Nuclear Power Nuclear fission is the process where a larger nucleus splits into two smaller nuclei and releases energy and a few neutrons in the process. Nuclear fusion is the process where two light nuclei combine to form a larger nucleus and release energy. This process occurs in stars. Commercial nuclear power reactors utilize the fission of U-235. Main components of a fission reactor: Fuel Rod rods which contain the fissile material typically enriched uranium ore (U-238 enriched with U-235) Moderator material that slows down a neutron released in a fission to a speed that increases the chance that the neutron will be absorbed and cause another fission typical material is water Control Rod material that absorbs neutrons to keep the fission rate at the correct value
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