Lecture Physics A2: Nuclear physics - PhD. Pham Tan Thi

Lecture Physics A2: Nuclear physics - PhD. Pham Tan Thi present the content fundamentals of atom and nuclei, nuclides and isotopes, magnetic moments, NMR and magnetic resonance imaging, stable nuclei and unstable nuclei,...
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Lecture Physics A2: Nuclear physics - PhD. Pham Tan Thi Nuclear Physics Pham Tan Thi, Ph.D.Department of Biomedical Engineering Faculty of Applied SciencesHo Chi Minh University of TechnologyFundamentals of Atom and Nuclei Nuclides and Isotopes• Electron and nucleon masses (12C nucleus is defined to have u = 12.00) Proton: mp = 1.007276 u Neutron: mn = 1.008665 u Electron: me = 0.000548580 u• The atomic number Z is the number of protons in the nucleus. The neutron number, N, is the number of neutrons in the nucleus. A = Z + N• A nuclide is an atom of a particular structure. Each element has nucleus with a specific number of protons.• Nuclide notation: A ZX A: Number of Nucleons Z: Number of Protons (Electrons) 12 1 0 1• Example: Carbon 1C; Neutron 0n; Electron -1e; Proton 1p Fundamentals of Atom and Nuclei✴ The number of nucleons A (also called the mass number) is the total number of protons and neutrons in the nucleus. The nucleon mass is measured in atomic mass unit, u, slightly less than the mass of the proton: 1 u = 1.6605 x 10-27 kg✴ The radius of most nuclei is given by R = RoA1/3, where Ro is experimentally determined as Ro = 1.2 x 10-15 m (1.2 fm)✴ All nuclei have approximately the same density.✴ Example: Common iron nuclei has mass number 56. Find the radius, approximate mass, and density of an iron nucleus. R = Ro A1/3 = (1.2 ⇥ 10 15 m)(56)1/3 = 4.6 fm 27 26 m = (56 u)(1.66 ⇥ 10 kg) = 9.3 ⇥ 10 kg 4 3 4 15 V = ⇡R = (4.6 ⇥ 10 m)3 = 4.1 ⇥ 10 43 m3 3 3 m 9.3 ⇥ 10 26 kg 17 3 Nucleus is 1013 times ⇢= = 43 = 2.3 ⇥ 10 kg/m the density of iron V 4.1 ⇥ 10 m3 Magnetic Moments• Like electrons, nucleons have 1/2-integer spin angular momentum, obeying the same relations as electron spin: p S=~ s(s + 1)• The z-component is itself a quantum number as electron spin: 1 Sz = ± ~ 2• The magnitude of the total angular momentum J of the nucleus is also neatly quantized as: p J =~ j(j + 1)with quantized z-component: Jz = mj ~ (mj = 0; ±1; ±2;…; ±j)• When A is even, j is an integer; but A is odd, j is a half-integer• Associated with the nuclear angular moment is a magnetic moment. In the case of a nucleus, the quantity of magnetic moment is nuclear magneton: eh Magnetic moment for the proton and neutron: µN = 2mp |msz | = 2.7928 µN |msz | = 1.9130 µN NMR and Magnetic Resonance ImagingNuclear Magnetic resonance and MRI use strong magnetic field to alignthe nuclear spins, then flips the spins with radio waves. When the radiowaves cease, the spins flip spontaneously and emit radio photons thatare measured.Nuclear Binding Energy The mass of the 12C atom, made up of 6 protons and 6 neutrons, defines the mass unit u, i.e. it has a mass of exactly 12 u. The individual masses of the protons and neutrons is 6(1.007276 u) + 6(1.008665 u) = 12.095646 u. The difference, 0.0956 u, when converted to energy E = mc2, is the binding energy EB of the nucleus. It is convenient to use the mass-energy equivalent of c2, which is 931.5 MeV/u, so that 0.0956 u => 89.1 MeV is the binding energy of 12C. It is the energy that must be added to separate the nucleons. The quantity EB/c2 is called the mass defect. EB = mc2 = (ZMH + N mn A Z M )c2 MH is the mass of a hydrogen atom, EB = mcnot 2 = just (ZMits H +proton, N mn A also Z M )c ...