Nuclear physics - Tran Thi Ngoc Dung

Nội dung text: Nuclear physics - Tran Thi Ngoc Dung

1. NUCLEAR PHYSICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. OUTLINE • BINDING ENERGY-BINDING ENERGY PER NUCLEON • NUCLEAR FORCE • RADIOACTIVITY-ALPHA, BETA, GAMMA DECAY • RADIOACTIVE CARBON DATING • NUCLEAR REACTIONS - FISSION, FUSION
3. NUCLEAR COMPONENTS Nucleus contains nucleons: protons and neutrons • Atomic number Z = number of protons • Neutron number N = number of neutrons • Mass number A = number of nucleons = Z + N • Each element has unique Z value • Isotopes of element have same Z, but different N and A values 1 2 3 1H, 1H,1H A Notion: Isotopes 16 17 18 Z X 8 O, 8 O, 8 O
4. RADIUS of a NUCLEUS 1/3 R RoA A=N+Z: Mass Number 15 R o 1.2 10 m 1.2fm
5. NUCLEAR DENSITY • All nuclei have approximately the same density 2.3 1017 kg / m3 Volume of the nucleus: : 4 4 4 V R 3 (R A1/3 )3 R 3A. 3 3 o 3 o Mass density 27 M mpA 1.67 10 nucleus 2.3.1017 kg / m3 4 4 4 R3 R3 .A (1.2 10 15 )3 3 3 o 3
6. Nucleus Charge and Mass Particle Charge Mass (kg) Mass (u) Mass (MeV/c2) Proton +e 1.6726 x10−27 1.007 276 938.28 Neutron 0 1.6750 x10−27 1.008 665 939.57 Electron −e 9.109 x 10−31 5.486x10−4 0.511 • Unified mass unit, u, defined using Carbon 12 • Mass of 1 atom of 12C ≡ 12 u 1 u = 1.660539 10 27 kg = 931.494 MeV / c2
7. NUCLEAR SPINS • Protons and neutrons are also spin ½ particle. • The magnitude of Spin angular momentum S of a nucleon: 3 S  s(s 1)  1 (1 1)  2 2 4 1 S  • The z component is z 2 In addition to the spin angular momentum, there may be orbital angular momentum associated with their motions within the nucleus. The total angular momentum 퐽 of the nucleus is the vector sum of the individual spin and orbital angular momenta of all the nucleons.
8. Total angular momentum • Total angular momentum of 1 nucleon:Ji L i Si • Total angular momentum of the nucleus: J  Ji Li Si i i i • The magnitude: of nuclear angular momentum: J j(j 1) • and z component: Jz m j (m j j, j 1, , j 1, j)
9. Total angular momentum j=nuclear spin • When A is even, j is an integer; 0,1,2,3 • When A is odd, j is a half interger. ½, 3/2 • All nuclides for which both Z and N are even have J=0, which suggests that pairing of particles with opposite spin components may be an important consideration in nuclear structure. • The total nuclear angular momentum number j is usually called the nuclear spin
10. Magnetic Moment • Associted with nuclear angular momentum is a magnetic moment. • Nuclear magneton: e 27 n 5.05078 10 J / T 2mp • The z component of the spin magnetic moment of the proton: sz 2.7928n proton • The neutron, which has zero charge, has a spin magnetic moment. The z component of the spin magnetic moment of the neutron:  1.9130 sz neutron n
11. Spin magnetic moment  • The proton has a positive charge; its spin magnetic moment  and spin angular momentum 푆 are parallel. • The neutron has no charge, its spin magnetic moment  and spin angular momentum 푆 are opposite ( as for a negative charge distribution) • The magnetic moment of an entire nucleus is typically a few nuclear magnetons. • When a nucleus is placed in an external magnetic field , there is an interaction energy : 푈 = −. = −
12. 8 7 U zB (2.7923)(3.152 10 eV / T)(2.3T) 2.025 10 eV 7 U zB 2.025 10 eV E 2.025 10 7 eV (2.025 10 7 eV) 4.05 10 7 eV 1.24 (m) 3.06m 4.05 10 7 (eV)
13. Binding Energy • The mass of nucleus is less than the mass of total nucleons. • The mass defect: M=Zmp+(A-Z)mn-M Where : M: Mass of the nucleus Or A M ZMH Nmn Z M • Where MH: mass of Z protons and Z electrons combines as Z neutral of atoms 1 to balance 1H A with Z electrons included in Z M neutral atom.
14. BINDING ENERGY Binding energy is energy required to separate nucleus into its constituents 2 A 2 EB M.c (ZMH Nmn Z M).c Binding energy per nucleon: E  B A
15. Atomic mass, u No Element Symbol Z 1u=1.660.10-27 kg (1 u)c2 = 931.5 MeV 1. Neutron n 0 1.008 665 2. Hydrogen 1H 1 1.007 825 M 28 1.007825 34*1.008665 61.928349 0.585361u 2 EB M.c 0.585361u 931.5 MeV / u 545.3MeV E 545.3MeV  B 8.795MeV / nucleon A 62
16. Binding energy per nucleon All stable nuclides have binding energies in the range of 7-9 MeV per nucleon.
17. The NUCLEAR FORCE The force that binds protons and neutrons together in the nucleus, despite the electrical repulsion of the protons is call nuclear force. It is an example of strong interaction. Some characteristics a) Nuclear force has short range, within 10^-15m. b) Nuclear force does not depend on charge: the binding n-n, p-p, p-n is the same. c) The nuclear force has saturation property. A nucleon cannot interact with all the other nucleon in the nucleus, but only with those few in its immediate vicinity d) The nuclear force depends on the spins of the nucleons. The nuclear force favors binding of pair of protons or neutrons with opposite spins and of pairs of pairs - pair of protons and a pair of neutrons, each pair having opposite spins.
18. NUCLEAR STABILITY and RADIOACTIVITY Segre chart showing neutron number For low mass number, the and proton number for stable nuclides numbers of protons and neutrons are approximately equal, N Z. The ratio N/Z increases with A, up to about 1.6 at large mass numbers, because of the increasing influence of the electrical repulsion of the protons. No nuclide with A>209 or Z>93 is stable.
19. Radioactivity • Unstable nuclei decay to more stable nuclei • Can emit 3 types of radiation in the process 4 particles: 2He nuclei  particles: e ore  rays: highenergy photons A positron (e+) is the antiparticle of the electron (e−) Fig. 29.5, p. 962
20. 1. Radioactivity Decay law • N (t): number of radioactive t nuclei in a sample at time t. N Noe • No: number of radioactive nuclei in a sample at time 0 t N • : decay constant o 2 T1/ 2 • The half life T1/2: is the time required for the number of N(t) radioactive nuclei to ln 2 0.693 decrease to one-half the  original number. T1/ 2 T1/ 2 1 • The mean lifetime Tmean T mean 
21. 2. ACTIVITY dN H N e t N H e t dt o o • ACTIVITY is the number of decay per unit time • Ho activity at time t=0. • The SI unit of activity is Bq (becquerel). 1Bq=1decay/s • Curi (Ci) : 1 Ci is equal to the activity of 1gram of radium 1Ci 3.7 1010 Bq
22. Decay Constant and Half-Life
23. 1 a) T mean  ln 2 0.693  2.95 10 8 s 1 T1/ 2 272day 24h / day 3600s / h 1 7 Tmean 3.39 10 s 392days 2.95 10 8 b)H N H 2 10 6 3.7 1010 N 2.51 1012 nuclei  2.95 10 8 t 6 2.95 10 8 365 24 3600 c)H Hoe 2 10 e 0.788Ci
24. Alpha ( ) Decay • Unstable nucleus emits particle (i.e., a helium nucleus) spontaneously • Mass of parent is greater than mass of daughter plus particle • Most of KE carried away by particle Fig 29.7, p. 966 A A 4 4 Z X Z 2Y+2 He
25. Beta()Decay • Involves conversion of proton to neutron or vice-versa • Involves the weak nuclear force • KE carried away by electron/antineutrino or positron/neutrino pair • Neutrinos: q = 0, m < 1 eV/c2, spin ½, very weak interaction with matter 1 1 A A 0 n 1p + e + ν Z X Z+1Y + e + ν 1 1 + A A + 1p 0 n + e + ν Z X Z 1Y + e + ν
26. Gamma (γ) Decay • Following radioactive decay, nucleus may be left in an excited state • Undergoes nuclear de-excitation: protons/neutrons move to lower energy level • Nucleus emits high energy photons (γ rays) • No change in A or Z results 12 12 5B 6C* e  12 12 6C* 6C 
27. Radioactive Carbon Dating 14 • Cosmic rays create14 12C Constant ratio of –12 C/ C (1.3×10 ) in atmosphere • Living organisms have same ratio • Dead organisms do not (no longer absorb C) 14 • T½ of C = 5730 yr • Measure decay rates, R ln RR) R Re t t 0 0 
28. m H N e t  N e t o  A N m 1g,R  A e t 0.255e t Bq / g Roe t Bg / g  0.255T 0.255 5730 365 24 3600 Number of C(14)per gram : N 1/ 2 o 0.693 0.693 6.65 1010 atomsC(14) / gram 1 Number of Cin1g :: N x6.023 1023 5.02 1022 / g 12 6.65 1010 ratio 1.32 10 12 5.02 1022 0.5gCarbon 174decay / h. H 0.5 R o exp( t)(Bq) T H 5730y 174 / 3600 t 1/ 2 ln( ) ln( ) 8019y 0.693 0.5 R o 0.693 0.5 0.255
29. Natural Radioactivity • Many radioactive elements occur in nature. For example, you are very slightly radioactive because of unstable nuclides such as carbon(C14) and potassium (K40) that are present throughout your body. • The decaying nucleus is usually called the parent nucleus; the resulting nucleus is the daughter nucleus. When a radioactive nucleus decays, the daughter nucleus may also be unstable. In this case a series of successive decays occurs until a stable configuration is reached. • Several such series are found in nature. The most abundant radioactive nuclide found on earth is the uranium isotope which undergoes a series of 14 decays, including eight emissions and six - emissions, terminating at a stable isotope of lead, 206 Pb.
30. Natural Radioactivity • Four radioactive series of naturally occurring radioactivity • Nuclear power plants use enriched uranium • Other series artificially produced
31. Alpha Decay 240 236 4 94 Pu 92U 2He
32. Beta Decay 228 0 228 88 Ra 1e 89Ac
33. Beta Plus Decay - Positron 230 0 230 91Pa 1e 90Th
34. Gamma Decay 240 240 0 94 Pu 94Pu 0
35. Nuclear Reactions • Accelerators can • Atomic and mass generate particle numbers (Z and A) must energies up to 1 TeV remain balanced • Bombard a nucleus with • Mass difference before energetic particles and after reaction • Nucleus captures the determines Q value particle – Exothermic: Q > 0 • Result is fission or fusion – Endothermic: Q < 0 • Endothermic requires incoming particle to have m KE KEmin = 1+ Q min M
36. Reaction energy A B C D 2 Q (MA MB MC MD )c When Q is positive, the total mass decreases and the total kinetic energy increases. Such a reaction is called an exothermic reaction. When Qis negative, the mass increases and the kinetic energy decreases, and the reaction is called an endothermic. In an endothermic reaction the reaction cannot occur unless the initial kinetic energy in the center-of-mass reference frame is at least as great as |Q|. That is, there is a threshold energy, the minimum kinetic energy to make an endothermic reaction go. m KEmin = 1+ Q M
37. Fusion and Fission
38. Fusion 2 3 4 1 1 H 1H 2 He 0n nuclear fusion is the process by which multiple like-charged atomic nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy.
39. Significant Nuclear Reactions - Fission 1 235 141 92 1 0 n 92U 56Ba 36Kr 30 n energy Nuclear fission differs from other forms of radioactive decay in that it can be harnessed and controlled via a chain reaction: free neutrons released by each fission event can trigger yet more events, which in turn release more neutrons and cause more fissions. The most common nuclear fuels are 235U (the isotope of uranium with an atomic mass of 235 and of use in nuclear reactors) and 239Pu (the isotope of plutonium with an atomic mass of 239). These fuels break apart into a bimodal range of chemical elements with atomic masses centering near 95 and 135 u (fission products).
40. Fission Bomb One class of nuclear weapon, a fission bomb is a fission reactor designed to liberate as much energy as possible as rapidly as possible A nuclear reactor is a device in which nuclear chain fission reactions are initiated, controlled, and sustained at a steady rate. Nuclear power plant