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

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

Nuclear Physics Pham Tan Thi, Ph.D. Department of Biomedical Engineering Faculty of Applied Sciences Ho Chi Minh University of Technology
Fundamentals 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 Imaging Nuclear Magnetic resonance and MRI use strong magnetic field to align the nuclear spins, then flips the spins with radio waves. When the radio waves cease, the spins flip spontaneously and emit radio photons that are 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 2 includes the electrons of the atom
Nuclides and Isotopes • Isotopes are nuclei which have the same number of protons but diﬀerent numbers of neutrons
Stable Nuclei and Unstable Nuclei Stable Nuclei: • Z:N ≈ 1:1 when Z is small (light) • Z:N ≈ 1:1.5 when Z is large (heavy) Unstable Nuclei: Most nuclei out of these ranges are unstable
Radioactive Decay Radioactive decay is the process by which an unstable atomic nucleus losses its energy by emitting radiation. • Parent nuclei decay to daughter ones having a higher nuclear binding. • An atom is radioactive when its nucleus is experienced re-arranged. • Radioactive decay is a process of emitting radiation. • Energy releases when decaying.
Radioactivity • Unstable nuclei decay to more stable nuclei • An isotope can emit 3 types of radiation in the process α particles : 42 He nuclei β particles : e − or e + γ rays : high energy photons A positron (e+) is the antiparticle of the electron (e-)
Alpha Decay An alpha particle (α) is a 4He nucleus, which is very stable. Large nuclei can decay by splitting into a smaller nucleus and an alpha particle, such as A (A 4) 4 ZX !(Z 2) Y +2 He Alpha decay is possible whenever the parent nuclide is more massive than the sum of the two daughter products.
Beta Decay • In a nucleus with too many protons or too many neutrons, beta decay takes place when one of the protons or neutrons is transformed into the other. • The number of nucleons, A, does not change after decaying process; the number of protons is increased or decreased. • There are three types of beta decays: beta-minus, beta-plus and electron capture.
Gamma Decay • A decaying process in which an unstable nucleus dissipates excess energy by a spontaneous electromagnetic process is called gamma (γ) decay. • No particles are ejected from the nucleus when it undergoes this type of decay. • Gamma ray has the same characteristic as X-ray does, but their origins are diﬀerent: ✴ X-ray originates from electromagnetic interaction process ✴ Gamma ray stems from changing energy levels
Characteristics of Decays
Activities and Half-lives • The half-life is the time for the number of radioactive nuclei to decrease to one-half of their original number. • Because the number of decays is proportional to the number of atoms available to decay, e.g. dN = N dt (minus sign indicates a loss), the number of remaining nuclei decrease exponentially. The solution to the above equation is found by re-arranging and integrating: dN N t = dt =) ln = t =) N = No e N No
Activities and Half-lives • To find the half-life, just determine when No t 1 N= and e = 2 2 ln2 t = t1/2 = • If you start with No nuclei, after a half-life you will have No/2, and after another half- life you will have No/4, etc. • The quantity 1/λ is called the mean lifetime. An established unit of radioactivity (-dN/dt) is called Curie: 1 Ci = 3.70 x 1010 decay/s In SI units, 1 decay/s is called Becquerel (Bq)
Example Activity of 57Co. The isotope 57Co decays by electron capture to 57Fe with a half-life of 272 d. The 57Fe nucleus is produced in an excited state, and it almost instantaneously emits gamma rays that we can detect. (a) Find the mean lifetime and decay constant for 57Co (b) If the activity of 57Co radiation sources is now 2.00 µCi, how many 57Co nuclei do the source contain? (c) What will be the activity after 1 year?
Radioactive Carbon Dating • Cosmic radiation protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen, the major constituent of the atmosphere. This neutron bombardment produces the radioactive isotope 14C. The radioactive 14C combines with oxygen to form CO2 and is incorporated into the cycle of living things. • The 14C forms at a rate which appears to be constant, so that by measuring the radioactive emissions from once-living matter and comparing its activity with equilibrium level of living things, a measurement of the time elapsed can be made. • Dead organisms/things do not absorb 14C. t ln(R/Ro ) R = Ro e =) t = • 14C decays to 14N by emitting a beta. T1/2 of 14C is 5730 years