Nuclear Basics Summer 2010

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basic nuclear science lecture
given to undergraduates for summer program at TINT
8 April 2010
Bangkok, Thailand

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Nuclear Basics Summer 2010

  1. 1. Basic Nuclear Physics Roppon Picha created: November 2005 updated: April 8, 2010
  2. 2. Dalton’s atoms (1808)
  3. 3. J.J. Thomson’s Experiment cathode rays = electrons (1897)
  4. 4. Rutherford, Geiger, Marsden 226 222 218 88 Ra → 86 Rn +α → α + 84 Po
  5. 5. rate of alpha scattering at angle θ from nucleus of charge Z: 2 Ze2 1 R(θ) ∝ 2 4 mα vα sin (θ/2)
  6. 6. Electron configuration Rutherford model (1911): Electrons orbit the nucleus like planets orbit the Sun. Bohr model of the atom (1913): Electrons stay in the atom on special orbits (orbitals). Experimentally verified by James Franck and Gustav Ludwig Hertz in 1914. Atoms only absorb certain “chunks” of energy.
  7. 7. Electron configuration principal quantum number: n = 1, 2, 3, . . . e− most strongly bound at n = 1. example: sodium (Na) has 11 electrons. In ground state, 2 electrons are in n = 1 level, 8 in n = 2, and 1 in n = 3.
  8. 8. Hydrogen e2 1 V (r ) = − 4π 0 r 13.6 En = − eV n2 (Bohr formula, 1913) hydrogenic (1 electron, Ze nuclear charge): 13.6Z 2 En = − n2
  9. 9. Sub configurations Besides n, we have orbital angular momentum quantum number l. l = 0, 1, 2, . . . , n − 1 letters: s, p, d, f, g, h, . . . Then, there is spin quantum number s.
  10. 10. Quantum angular momentum total angular momentum quantum number j: j=s+l values jump in integer steps: |l − s| ≤ j ≤ l + s
  11. 11. Quantum angular momentum example: for the electron, s = 1/2. if l = 1, what are possible values of j? s = 1/2 and l = 3? What are all possible j values for electron in n = 4 level?
  12. 12. Proton (1919) was discovered by Rutherford. α+N→H+O Protos = first
  13. 13. Chadwick’s Neutron Discovery • Existence suggested since 1920 by Rutherford. • Finally found via experiments in 1932. 9 4 Be5 +4 He2+ 2 2 −→ 12 6 C +1 n1 0 or (α, n) reaction mass: neutron 939.6 MeV/c2 ≈ proton 938.3 MeV/c2
  14. 14. Neutron energy Fast neutrons = high-energy neutrons. E > 1 eV. Thermal neutrons = those with average thermal energy corresponding to room temperature (T = 300 K). 3 1 Eth = kB T ≈ eV 2 40 where kB = 1.38 × 10−23 J/K.
  15. 15. Energy and Velocity For a nucleon of kinetic energy 15 MeV, the velocity can be calculated via 1 T = mv 2 2 2T 2 · 15 v= ≈c ≈ 0.18c m 938 de Broglie wavelength of this nucleon is h 4.1 × 10−21 MeV s λ= = ≈ 7.3 fm mv 938MeV c−2 · 0.18c
  16. 16. Accelerated Charge
  17. 17. EM radiation Electric field far away does not know of particle’s movement. The electric field form a wavefront consisting radial (Coulomb) and transverse components. q 2 a2 radiated power = P = Larmor’s equation 6π 0 c 3
  18. 18. Electromagnetic Spectrum
  19. 19. p++
  20. 20. Region of Stability
  21. 21. Binding Energy per Nucleon
  22. 22. Binding energy binding energy of most nuclei ∼ 8 MeV/nucleon electrons are bound at ∼ 10 eV to atoms.
  23. 23. Separation Energy removing a proton: A A−1 Z XN −→ Z −1 YN removing a neutron: A A−1 Z XN −→ Z YN−1 Separation energy (S) is the difference between binding energies (B) of initial nucleus and final nucleus.
  24. 24. Separation Energy S > 0 when we change a stable nucleus (high B) into a less stable nucleus (low B). B = ( mconstituents − matom )c 2 S ≡ Bi − Bf Sp = B(A XN ) − B(A−1 YN ) Z Z −1 Sn = B(A XN ) − B(A−1 YN−1 ) Z Z
  25. 25. Ionization vs. Separation
  26. 26. Quantum behaviors Subatomic particles can be described by quantum mechanics. States are represented by wave function ψ(x, t). Particles = Wave packets = superpositions of waves.
  27. 27. Wave functions Wave = non-localized state. ∆x · ∆p > (Heisenberg uncertainty relation) To get the wave function and its evolution, solve Schrodinger’s equation: 2 ∂ψ i = − +V ψ ∂t 2m
  28. 28. Wave function Normalization: ∞ |ψ(x, t)|2 dx = 1 −∞ At any given time, the particle has to be somewhere. expectation values: x = ψ ∗ (x)ψ dx p = ψ ∗ (p)ψ dx
  29. 29. Wave properties de Broglie wavelength of a (non-zero mass) particle of momentum p h λ= p Experimental verification: Davisson and Germer (1954).
  30. 30. Davisson and Germer used 54-eV electron beam to scatter of a nickel crystal. An interference peak was observed, similar to Bragg peak in x-ray diffraction.
  31. 31. Photons ∼ 1900: Blackbody radiation study led Planck to think about nature of electromagnetic energy. 1905: Einstein proposed that light consists of photons, each possessing a certain lump of energy. Total energy = multiples of this number.
  32. 32. Energy Planck-Einstein relation gives energy of a photon: hc E = hν = ω = λ ν and ω are frequency and angular frequency, respectively.
  33. 33. Energy h = 6.63 × 10−34 J s = 4.14 eV s for λ given in angstrom: 12.4 E= keV λ Characteristic radiation of atoms which has only certain values are due to the fact that the atoms only exist in certain stable states of discrete energies.
  34. 34. Photon interactions excitation (and de-excitation) hν + Am ↔ An ionization (and recombination) hν + A ↔ A+ + e−
  35. 35. Fermions and Bosons Protons, neutrons, and electrons belong to the fermion family. Quarks and leptons are also fermions. They have odd half-integer spins: s = 1/2, 3/2, 5/2, . . .. Bosons have integer spin: s = 0, 1, 2, . . .. examples: photons (s = ±1) and 4 He atoms (s = 0)
  36. 36. Periodic table Electrons are identical fermions. At a given orbital (n, l, m), only two electrons can occupy the same state (one spin-up, one spin-down) For each l, there are 2l + 1 values of ml . For each (l, ml , there is two spin states (ms = ± 1 ). 2 Exercise: What are maximum number of electrons for l = 0, 1, 2, 3?
  37. 37. Periodic table shows an integer increase of protons and electrons. Shells are filled, from low to high energies. Ground-state configs: • H: (1s 1 ) • He: (1s 2 ) • Li: (He)(2s 1 ) • Be: (He)(2s 2 ) • B: (He)(2s 2 )(2p 1 ) • ...
  38. 38. information about a radioisotope.
  39. 39. Decay Law dN(t) = −λN(t) dt t is time. N(t) is number of nuclei. λ is decay constant. solution: N(t) = N0e−λt N0 = number of nuclei at the starting time. decay constant is inversely proportional to the half-life: ln 2 λ= t1/2
  40. 40. A parent nuclide decays and yields a daughter nuclide. increase in number of daughter (D) = decrease in number of parents (P) Df − Di = Pi − Pf
  41. 41. Decay constant Decays aren’t always 1-to-1: A → B (55% of the time) → C (40%) → D (5%) For branched decays, the total decay constant is just the sum of each mode constant: λtot = λ1 + λ2 + λ3 + . . .
  42. 42. Lifetime For a given decay constant λ, the lifetime of the state is 1 τ= λ It is the time taken the state to drop from N0 to N0 /e ≈ 0.37N0 . branched decays: 1 τ= λ1 + λ2 + . . .
  43. 43. Activity dN A≡− = λN = −λN0 e−λt = A0 e−λt dt A is also called “decay rate” or “disintegration rate.” units: becquerel (1 s−1 ) or curie (3.7 × 1010 s−1 )
  44. 44. Mysterious rays Henri becquerel discovered radioactivity from uranium ore in 1896. At Cambridge, Rutherford studied these unknown rays and published results in 1899. Those that got absorbed by a sheet of paper or a few cm of air was named alpha rays. The more penetrating ones were called beta rays.
  45. 45. Alpha Decay Alpha (α) = 2p&2n bound state Process: A A−4 Z XN −→ Z −2 YN−2 + 4 He2 2
  46. 46. Examples: 226 222 88 Ra138 → 86 Rn136 + α 238 234 92 U146 → 90 Th144 + α mX c 2 = (mY c 2 + TY ) + (mα c 2 + Tα ) Q ≡ (mi − mf )c 2 = (mX − mY − mα )c 2
  47. 47. Alpha emitters with large Q tend to have short half-lives. Z ln λ(E) = a − b √ E Geiger-Nuttall law. λ is the decay constant; a and b are constants; Z is the atomic number; E is the decay energy.
  48. 48. Beta Decay W. Pauli: There must be a neutrino. (1930) Cowan and Reines observed it. (1956)
  49. 49. Beta Decay Processes: n → p + e− + νe ¯ β − decay p → n + e+ + νe β + decay (rare) p + e− → n + νe e capture (ε) Examples: 234 234 − 90 Th144 → 91 Pa143 + e + νe ¯ 53m 53 + 27 Co → 26 Fe + e + νe 15 − 15 O+e → N + νe
  50. 50. X-ray Charged particles that decelerate create electromagnetic radiation. This process is known as bremsstrahlung. Photons can excite or ionize atoms. Subsequent atomic transitions can produce additional X-ray photons. This process is called X-ray fluorescence. If an atomic electron absorbs such X-ray photon, it can be ejected. These electrons are called Auger (oh-zhay) electrons.
  51. 51. Gamma Decay A year after Rutherford discovered α and β rays, Paul Villard discovered a more penetrating radiation from radium. This is the gamma (γ) ray. Excited nuclear states can decay via γ emission. Typical energies ∼ 0.1 − 10 MeV. Examples: 99m 99 43 Tc → 43 Tc + γ isomeric transition − 60 27 Co → 60 28 Ni + e + νe + γ ¯ with β −
  52. 52. Internal conversion An excited nucleus can interact with an orbital electron, transferring energy Eex . The electron gets ejected with energy Ee = Eex − Eb where Eb is the binding energy of the electron.
  53. 53. The gamma decay and internal conversion decay contribute to total decay probability: λ = λγ + λe
  54. 54. Radiation Units quantity description units activity (A) decay rate curie (Ci), becquerel (Bq) exposure (X ) air ionization roentgen (R), coulomb/kg absorbed dose (D) absorbed energy rad, gray (Gy) dose equivalent (DE) bio. effects rem, sievert (Sv)
  55. 55. Quiz 1. What kind of radiation does not come from a nucleus? [choices: α, β, x-ray, γ] 2. Be-7 decays by capturing an electron. What is the resulting nuclide? 3. 15.1% of natural samarium is 147 Sm, which decays by emitting α. 10 grams of natural samarium gives 120 α per second. Calculate activity per gram of 147 Sm.
  56. 56. Reaction Cross Section for reaction a + X −→ Y + b reaction rate σ= fluxincident · densitytarget rate of detecting b = (flux of a) · (X areal density)
  57. 57. Nuclear Reactions: First reaction in lab
  58. 58. Creating new nuclides making light radionuclides: 14 N + n →14 C +1 H 55 Mn +2 H →55 Fe + 2n 59 Co + n →60 Co + γ making Np-239 (transuranic) 238 U + n →239 U 239 U →239 Np + e− + νe ¯
  59. 59. Balancing nuclear equations What is x in each of these nuclear reactions? 197 12 79 Au +6 C → 206At + x 85 32 4 16 S + He → x +γ 27 13 Al + p → x +n 4 He +17 N 7 → x +1 H
  60. 60. EM interactions Main processes: Photoelectric absorption Compton scattering Pair production
  61. 61. Intensity attenuation: I(x) = I(0)e−µx half-value layer = thickness that reduces intensity by 50%.
  62. 62. Producing radionuclides Ways to do it: • Reactors • Accelerators • Generators
  63. 63. Reactors A X +n → → Longer irradiation time → higher specific activity.
  64. 64. Examples: 130 51 Te +n → → 6 3 Li +n →α+t as fission products: 85 133 90 99 137 36 Kr, 54 Xe, 38 Sr, 42 Mo, 55 Cs
  65. 65. Accelerators Usual projectiles: p, d, α Examples: 20 18 10 Ne(d, α) 9 F 76 76 34 Se(p, n) 35 Br 35 38 17 Cl(α, n) 19 K
  66. 66. Generators Suppose you want to use a short-lived nuclide produced from a reactor. But you are far away from the reactor. What can you do? Prepare the parent nuclide which has longer half-life, in a device that can separate the daughter from the parent. Examples: 44 44 22 Ti (t1/2 = 6 y) ⇒ 21 Sc (t1/2 = 3.9 h) 83 83m 37 Rb (86 d) ⇒ 36 Kr (1.8 h) 99 99m 42 Mo (66 h) ⇒ 43 Tc (6 h)
  67. 67. the End

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