Physics A2 - NuclearPhysics - Huynh Quang Linh

Nội dung text: Physics A2 - NuclearPhysics - Huynh Quang Linh

1. Intro to Nuclear Physics 1
2. About Units ❑ Energy - electron-volt l 1 electron-volt = kinetic energy of an electron when moving through potential difference of 1 Volt; o 1 eV = 1.6 × 10-19 Joules o 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV o 1 MeV = 106 eV, 1 GeV= 109 eV, 1 TeV = 1012 eV ❑ mass - eV/c2 o 1 eV/c2 = 1.78 × 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 × 10-28 kg m/s o momentum of baseball at 80 mi/hr 5.29 kgm/s 9.9 × 1027 eV/c ❑ Distance o 1 femtometer (“Fermi”) = 10-15 m 3
3. 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
4. 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
5. 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 ½), 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 ½ Pauli principle 9 only two identical nucleons per eng. level
6. 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
7. 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 ½, 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 ½, magnetic moment -1.9 eħ/2mn 13
8. 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
9. 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
10. 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
11. 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., 84Po→ 82Pb+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→44Rb + e + 43 43 b+ decay: A A + Z X →Z -1Y + e + 12 12 + e.g., 7 N→ 6 C + e + 21
12. 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
13. 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
14. EB/A vs A 27
15. 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,
16. 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
17. Nuclear Energy - Fission + about 200 MeV energy 33
18. Fission 35
19. 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
20. 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