Intro to Nuclear Physics - Huynh Quang Linh

Nội dung text: Intro to Nuclear Physics - Huynh Quang Linh

1. Intro to Nuclear Physics 1
2. Nuclear Physics Topics  Composition of Nucleus  features of nuclei  Nuclear Models  nuclear energy  Fission  Fusion  Summary 2
3. About Units  Energy - electron-volt  1 electron-volt = kinetic energy of an electron when moving through potential difference of 1 Volt; o 1 eV = 1.6 ì 10-19 Joules o 1 kW•hr = 3.6 ì 106 Joules = 2.25 ì 1025 eV o 1 MeV = 106 eV, 1 GeV= 109 eV, 1 TeV = 1012 eV  mass - eV/c2 o 1 eV/c2 = 1.78 ì 10-36 kg o electron mass = 0.511 MeV/c2 o proton mass = 938 MeV/c2 = 0.938 GeV/ c2 o neutron mass = 939.6 MeV/c2  momentum - eV/c: o 1 eV/c = 5.3 ì 10-28 kg m/s o momentum of baseball at 80 mi/hr 5.29 kgm/s 9.9 ì 1027 eV/c  Distance o 1 femtometer (“Fermi”) = 10-15 m 3
4. Radioactivity  Discovery of Radioactivity  Antoine Becquerel (1896): serendipitous discovery of radioactivity: penetrating radiation emitted by substances containing uranium  A. Becquerel, Maria Curie, Pierre Curie(1896 – 1898): o also other heavy elements (thorium, radium) show radioactivity o three kinds of radiation, with different penetrating power (i.e. amount of material necessary to attenuate beam): . “Alpha (a) rays” (least penetrating – stopped by paper) . “Beta (b) rays” (need 2mm lead to absorb) . “Gamma (g) rays” (need several cm of lead to be attenuated) o three kinds of rays have different electrical charge: a: +, b: -, g: 0  Identification of radiation:  Ernest Rutherford (1899) o Beta (b) rays have same q/m ratio as electrons o Alpha (a) rays have same q/m ratio as He o Alpha (a) rays captured in container show He-like emission spectrum4
5. Proton  “Canal rays”  1898: Wilhelm Wien: opposite of “cathode rays”  Positive charge in nucleus (1900 – 1920)  Atoms are neutral o positive charge needed to cancel electron’s negative charge o Rutherford atom: positive charge in nucleus  periodic table realized that the positive charge of any nucleus could be accounted for by an integer number of hydrogen nuclei protons 5
6. Neutron  Walther Bothe 1930: 9  bombard light elements (e.g. 4 Be) with alpha particles neutral radiation emitted  Irốne and Frederic Joliot-Curie (1931)  pass radiation released from Be target through paraffin wax protons with energies up to 5.7 MeV released  if neutral radiation = photons, their energy would have to be 50 MeV puzzle  puzzle solved by James Chadwick (1932):  “assume that radiation is not quantum radiation, but a neutral particle with mass approximately equal to that of the proton”  identified with the “neutron” suggested by Rutherford in 1920  observed reaction was: 9 13 a (24He++) + 4 Be 6 C* 13 12 6 C* 6 C + n 6
7. Beta decay neutrino  Beta decay puzzle : o decay changes a neutron into a proton o apparent “non-conservation” of energy o apparent non-conservation of angular momentum  Wolfgang Pauli predicted a light, neutral, feebly interacting particle (called it neutron, later called neutrino by Fermi) 7
8. Positron  Positron (anti-electron)  Predicted by Dirac (1928) needed for relativistic quantum mechanics  existence of antiparticles doubled the number of known particles!!! Positron track going upward through lead plate  P.A.M. Dirac  Nobel Prize (1933)  member of FSU faculty (1972-1984)  one of the greatest physicists of the 20th century 8
9. Structure of nucleus  size (Rutherford 1910, Hofstadter 1950s): 1/3 -15  R = r0 A , r0 = 1.2 x 10 m = 1.2 fm;  i.e. ≈ 0.15 nucleons / fm3  generally spherical shape, almost uniform density;  made up of protons and neutrons  protons and neutron “nucleons”; are fermions (spin ẵ), have magnetic moment  nucleons confined to small region (“potential well”)  occupy discrete energy levels  two distinct (but similar) sets of energy levels, one for protons, one for neutrons  proton energy levels slightly higher than those of neutrons (electrostatic repulsion)  spin ẵ Pauli principle 9 only two identical nucleons per eng. level
10. Nuclear Sizes - examples 1 3 -15 r ro (A ) ro = 1.2 x 10 m Find the ratio of the radii for the following nuclei: 1H, 12C, 56Fe, 208Pb, 238U 1 1 1 1 1 13 :123 : 563 : 2083 : 2383 1 : 2.89 : 3.83 : 5.92 : 6.20 10
11. A, N, Z  for natural nuclei:  Z range 1 (hydrogen) to 92 (Uranium)  A range from 1 ((hydrogen) to 238 (Uranium)  N = neutron number = A-Z  N – Z = “neutron excess”; increases with Z  nomenclature: A A  Z XN or XN or A X or X-A 11
12. Atomic mass unit  “atomic number” Z Number of protons in nucleus  Mass Number A Number of protons and neutrons in nucleus Atomic mass unit is defined in terms of the 12 mass of 6C, with A = 12, Z = 6: 12 1 amu = (mass of 6C atom)/12 1 amu = 1.66 x 10-27kg 1 amu = 931.494 MeV/c2 12
13. Properties of Nucleons  Proton  Charge = 1 elementary charge e = 1.602 x 10-19 C  Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u = 1836 me  spin ẵ, magnetic moment 2.79 eħ/2mp  Neutron  Charge = 0  Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u = 1839 me  spin ẵ, magnetic moment -1.9 eħ/2mn 13
14. Nuclear masses, isotopes  Nuclear masses measured, e.g. by mass spectrography  masses expressed in atomic mass units (amu), energy units MeV/c2  all nuclei of certain element contain same number of protons, but may contain different number of neutrons  examples:  deuterium, heavy hydrogen 2D or 2H; heavy water = D2O (0.015% of natural water)  U- 235 (0.7% of natural U), U-238 (99.3% of natural U), 14
15. Nuclear Masses, binding energy  Mass of Nucleus Z(mp) + N(mn)  “mass defect” m = difference between mass of nucleus and mass of constituents  energy defect = binding energy EB 2 EB = m c  binding energy = amount of energy that must be invested to break up nucleus into its constituents  binding energy per nucleon = EB /A 15
16. Nuclear Binding Energy  The difference between the energy (or mass) of the nucleus and the 1 amu = 931.5 MeV energy (or mass) of its constituent neutrons and m(proton) 1.00782 protons. m(neutron) 1.00867  = the energy needed to A = 56 break the nucleus apart.  Average binding energy Z = 26 per nucleon = total binding energy divided by N = 30 the number of nucleons Mass (amu) 55.92066 (A). Ebinding (MeV) -505.58094  Example: Fe-56 EB/A(MeV) -9.02823 16
17. Problem – set 4  Compute binding energy per nucleon for 4  2He 4.00153 amu 16  8O 15.991 amu 56  26Fe 55.922 amu 235  92U 234.995 amu  Is there a trend?  If there is, what might be its significance?  note: 1 amu = 931.5 MeV/c2 m(proton) = 1.00782 amu m(neutron)=1.00867 amu 17
18. Binding energy per nucleon  18
19. Nuclear Radioactivity  Alpha Decay AZ A-4(Z-2) + 4He o Number of protons is conserved. o Number of neutrons is conserved.  Gamma Decay AZ* AZ + g o An excited nucleus loses energy by emitting a photon. 19
20. Beta Decay  Beta Decay  AZ A(Z+1) + e- + an anti-neutrino o A neutron has converted into a proton, electron and an anti-neutrino.  Positron Decay  AZ A(Z-1) + e+ + a neutrino o A proton has converted into a neutron, positron and a neutrino.  Electron Capture  AZ + e- A(Z-1) + a neutrino o A proton and an electron have converted into a neutron and a neutrino. 20
21. Radioactivity  Several decay processes: Electron capture: A - A a decay: A A-4 4 Z X + e Z -1Y + Z X Z -2Y +2He 210 206 4 12 - 12 e.g., 84 Po 82 Pb+2He e.g., 7 N + e 6 C + g b- decay: decay: ~ A * A A A - Z X Z X +g Z X Z +1Y + e + ~ 99 * 99 99 99 - e.g., Tc Tc +g (140keV) e.g., 43Tc 44 Rb + e + 43 43 b+ decay: A A + Z X Z -1Y + e + 12 12 + e.g., 7 N 6 C + e + 21
22. Law of radioactive decay dN  Activity A = number of A . decays per unit time dt  decay constant  = probability of decay per unit time dN -N.  Rate of decay  number N dt of nuclei -t  Solution of diff. equation N(t) N0e . (N0 = nb. of nuclei at t=0)  Mean life  = 1/  t e-t dt t dN 1  0 dN  e-t dt 0 22
23. Nuclear decay rates Nuclear Decay 1000.0 800.0 -t 600.0 N(t) N0e . 400.0 At t = 1/, 200.0 Nuclei Remaining Nuclei N is 1/e (0.368) 0.0 of the original 0.0 1.0 2.0 3.0 4.0 5.0 amount Time(s) 23
24. Nuclear (“strong”) force  atomic nuclei small about 1 to 8fm  at small distance, electrostatic repulsive forces are of macroscopic size (10 – 100 N)  there must be short-range attractive force between nucleons the “strong force”  strong force essentially charge-independent  “mirror nuclei” have almost identical binding energies  mirror nuclei = nuclei for which n p or p n (e.g. 3He and 3H, 7Be and 7Li, 35Cl and 35Ar); slight differences due to electrostatic repulsion  strong force must have very short range – << atomic size, otherwise isotopes would not have same chemical properties 24
25. Strong force 2  range: fades away at distance ≈ 3fm  force between 2 nucleons at 2fm distance ≈ 2000N  nucleons on one side of U nucleus hardly affected by nucleons on other side  experimental evidence for nuclear force from scattering experiments;  low energy p or a scattering: scattered particles unaffected by nuclear force  high energy p or a scattering: particles can overcome electrostatic repulsion and can penetrate deep enough to enter 25 range of nuclear force
26. N-Z and binding energy vs A  small nuclei (A 60)  adding more nucleons does not increase overall cohesion due to nuclear attraction  Repulsive electrostatic forces (infinite range!) begin to have stronger effect  N-Z must be bigger for heavy nuclei (neutrons provide attraction without electrostatic repulsion  heaviest stable nucleus: 209Bi – all nuclei heavier than 209Bi are unstable (radioactive) 26
27. EB/A vs A 27
28. Nuclear Models – liquid drop model  liquid drop model (Bohr, Bethe, Weizsọcker):  nucleus = drop of incompressible nuclear fluid.  fluid made of nucleons, nucleons interact strongly (by nuclear force) with each other, just like molecules in a drop of liquid.  introduced to explain binding energy and mass of nuclei  predicts generally spherical shape of nuclei  good qualitative description of fission of large nuclei  provides good empirical description of binding energy vs A 28
29. Shell Models  assume nucleons move inside nucleus without interacting with each other  Fermi- gas model:  Protons and neutrons move freely within nuclear volume, considered a rectangular box  Protons and neutrons are distinguishable and so move in separate potential wells  Shell Model  formulated (independently) by Hans Jensen and Maria Goeppert-Mayer  Each nucleon (proton or neutron) moves in the average potential of remaining nucleons, assumed to be spherically symmetric.  Also takes account of the interaction between a nucleon’s spin and its angular momentum (“spin-orbit coupling”)  derive “magic numbers” (of protons and/or neutrons) for which 29 nuclei are particularly stable: 2, 8, 20, 28, 50, 82, 126,
30. Fermi-Gas Model of Nucleus  Ground State Potential well  In each potential well, the lowest energy states are occupied.  Because of the Coulomb repulsion the proton well is shallower than that of the neutron.  But the nuclear energy is  Therefore, as Z increases we minimized when the maximum would expect nuclei to contain energy level is about the progressively more neutrons same for protons and than protons. neutrons  U has A = 238, Z = 92 30
31. Collective model  collective model is “eclectic”, combining aspects of other models  consider nucleus as composed of “stable core” of closed shells, plus additional nucleons outside of core  additional nucleons move in potential well due to interaction with the core  interaction of external nucleons with the core agitate core – set up rotational and vibrational motions in core, similar to those that occur in droplets 31  gives best quantitative description of nuclei
32. Nuclear energy  very heavy nuclei:  energy released if break up into two medium sized nuclei  “fission”  light nuclei:  energy released if two light nuclei combine “fuse” into a heavier nucleus – “fusion” 32
33. Nuclear Energy - Fission + about 200 MeV energy 33
34. Nuclear reactor – Nuclear Power Plant 34
35. Fission 35
36. Nuclear Fusion 36
37. Sun’s Power Output Unit of Power  1 Watt = 1 Joule/second  100 Watt light bulb = 100 Joules/second  Sun’s power output  3.826 x 1026 Watts  exercise: calculate sun’s power output using Stefan-Boltzmann law (assume sun is a black body) 37
38. The Proton-Proton Cycle 1H + 1H → 2H + e+ +  e+ + e- → g + g 2 1 3 1 pp collision in 1022 → fusion! H + H → He + g 3He + 3He → 4He + 1H + 1H 4H → 4He Deuterium creation 3He creation 4He creation 38
39. Summary  nuclei made of protons and neutrons, held together by short-range strong nuclear force  models describe most observed features, still being tweaked and modified to incorporate newest observations  no full-fledged theory of nucleons yet  development of nuclear theory based on QCD has begun  nuclear fusion is the process of energy production of Sun and other stars  we (solar system with all that’s in it) are made of debris from dying stars 39