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2008 Summerresidentlecture Atoms Mass and Energy Units Nucleus: ~10-14 m diameter and Introduction to Nuclear ~1017 kg/m3 Mass-Energy Equivalence Electron clouds: ~10-10 m diameter Physics and Nuclear Decay (= size of atom) Mass water molecule: ~10-10 m diameter atomic mass unit, u (or amu): mass of 12C ≡ 12.000000 u ~103 kg/m3 1 u = 1.660540 x 10-27 kg = 931.494 x 106 eV/c2 Nucleons (protons and neutrons) are ~10,000 times Energy smaller than the atom, and ~1800 times more massive Larry MacDonald Electron volt, eV ≡ kinetic energy attained by an electron accelerated through 1.0 volt than electrons. 22 May 2008 (electron size < 10-22 m (only an upper limit can be estimated)) 1 eV = 1.6 x10-19 J 2 Nuclear and atomic units of length E = mc c = 3 x 108 m/s -15 10 = femtometer (fm) speed of light 10-10 = angstrom (Å) Molecules -27 2 Course website (Nuclear Medicine Imaging) mass of proton, mp = 1.6724x10 kg = 1.007276 u = 938.3 MeV/c -27 2 mostly empty space mass of neutron, mn = 1.6747x10 kg = 1.008655 u = 939.6 MeV/c http://depts.washington.edu/uwmip/ Hecht, Physics, 1994 -31 2 Water mass of electron, me = 9.108x10 kg = 0.000548 u = 0.511 MeV/c (wikipedia) 22 May 2008 2 22 May 2008 3 Elements Named for their number of protons Nuclide Groups/Families N vs. Z Chart of Nuclides X = element symbol Z (atomic number) = number of protons in nucleus N > Z for the majority A nuclide is a nucleus with a specific Z and A (N = Z for low Z elements) N = number of neutrons in nucleus A A A ~1500 nuclides exist A (atomic mass number) = Z + N Z X N Z X X [A is different than, but approximately equal to the atomic (Periodic Table typically lists distinct Z) The line of stability (gold band) weight of an atom] Examples; oxygen, lead represents the stable nuclei. A X 16 208 Nuclides with the same Electrically neural atom, Z N has Z electrons in its O Pb Distribution of stable nuclei: atomic orbit. Otherwise it is ionized, and holds net electric 8 8 82 126 Z (#protons) are Isotopes Z N #stable nuclei charge. even even 165 N (#neutrons) are Isotones even odd 57 odd even 53 Z A (#nucleons) are Isobars odd odd 4 isobars A nuclide with the same Z and A (& thus also N) can also exist 279 stable nuclei exist isotones in different (excited & ground) states; these are Isomers (all have Z < 84) isotopes ~1200 unstable (radioactive) (65 natural, remaining are human-made) Hecht, Physics, 1994 22 May 2008 4 22 May 2008 5 22 May 2008 6 [email protected] 1 Nuclear Shell Structure Binding Energy Schematic energy diagrams Radioactive Decay • Similar to atomic structure, the nucleus can be E=0: particle is unbound (free) The mass of a nuclide is less than the mass of the sum of the constituents. modeled as having quantized allowed energy states E<0: particle is bound (e.g. in Unstable nuclei change (decay) towards stable states (shells) that the nucleons occupy. The difference in energy is the binding energy. nucleus, in an atom) The transformation involves emission of secondary particles: • The lowest energy state is the ground state. E>0: free & has excess energy (can be potential or kinetic) The consequence is that energy is liberated when nucleons join to form a • Nuclei can exist in excited states with energy greater nuclide. Radiation than the ground state. E • Excited nuclear states that exist for > 10-12 sec. are The binding energy per nucleon dictates results when nuclides break apart A A " [*] Z X! Z Y + W + Q metastable states (isomeric). (fission) or fuse together (fusion) " • Nucleons held together by the ‘strong force’; short range, but strong. X = parent nucleus, Y = daughter nucleus [possibly excited *], W = radiation particle(s), Q = additional energy liberated in the decay; Q is • This overcomes the repulsive electrostatic force of shared between the X, Y, and W particles. Y is frequently unstable itself. similar charged protons (keep in mind that binding energies are • Also similar to atomic theory: thought of as negative, as in energy level Conservation principles: → Electrons swirl around in clouds about the nucleus; diagrams on previous • Energy (equivalently, mass) likewise, the nucleus is a dynamic swirl of nucleons. slide) • linear momentum → Nucleons, like electrons, are paired in energy states - each with opposite spin. • angular momentum (including intrinsic spin) → Closed electron shells lead to chemically inert atoms. Bushberg • charge Magic numbers of nucleons (analogous to closed are all conserved in radioactive transitions shells) form particularly stable nuclei. 22 May 2008 Hecht, Physics, 19974 22 May 2008 8 22 May 2008 9 Radioactive Decay Processes Decay Time Alpha Decay The decay processes are named for the (primary) radiation The rate at which radionuclides decay is governed by a An alpha particle is the same as a helium nucleus; particle emitted in the transition: characteristic decay time constant, " (two protons and two neutrons) (units of " are inverse-time, i.e. frequency or rate) 4 2 • alpha A A"4 + X Y Q !"t !=2 He Z ! Z"2 +# + N t = N e ( ) 0 • beta N(t) = number of radionuclides at time t General form of alpha decay process A A ± N = number at time t = 0 X! Y + " + # + Q 0 isobaric Z Z!1 " = characteristic decay time constant A A"4 4 +2 + X! Y+ He + Q alternative mechanism to ! decay is electron capture Z Z"2 2 The half-life, T1/2, is the time it takes for a sample to decay to one-half of its original number, or half of its original activity. • gamma A[ m] X[*] A X • Alpha particle always carries Q energy as kinetic energy (monoenergetic) Z ! Z + " ln(2) 0.693 isomeric T1/ 2 = = • Alpha dec ay occurs with heavy nuclides (A > 150) ! ! alternative mechanism is internal conversion • Commonly followed by isomeric emission of photons, " t % • which can also result in electron emission (see internal conversion slide) !$ ' The ionization (net charge) on particles can also be specified (upper-right) # T1 / 2 & N t = N0 2 ( ) 22 May 2008 10 22 May 2008 11 22 May 2008 12 [email protected] 2 Beta Decay Electron Capture Gamma Emissions - A beta(minus, ! ) particle is an electron (or, it is indistinguishable from an An alternative (and competing mechanism) to !+ decay is electron capture. electron). Gamma decay is an isomeric transition that follows the occurrence of alpha In electron capture, a proton is converted to a neutron, as in !+ decay, or beta decay. + There are also beta(plus, ! ) particles. These are indistinguishable from + however, rather than emitting a ! , an orbital electron (usually from inner A[ m] [*] A electrons, except with positive charge (of the same magnitude). X X electron shells) is captured by the nucleus, conversion of a proton to a Z ! Z + " The general form of !-, !+ decay: neutron occurs, and a neutrino (and additional energy, Q) are emitted from the decay process: The parent in this case (which is the daughter of the preceding $ or ! decay, or electron capture) can be in an excited state, * ,that (essentially) immediately A A # A A + A X e! A Y Q Z X!Z+1Y + " + $ + Q Z X!Z"1Y + # + $ + Q Z + "Z!1 + # + transitions to a lower state via emission of a gamma, or it can be in a metastable state m, which can have a life-time of between 10-12 sec. and ~600 18 18 + Capture of an electron creates a vacancy in an inner electron shell, which is years. De cay of metastable states also follow the exponential decay law, and e.g. 9 F! 8 O + " + # + 0.635MeV filled by another electron from a higher shell. This results in characteristic x- thus have characteristic decay times. rays, or Auger electrons. In !- decay, a nuclear neutron is converted into a proton (Z#Z+1) In !+ decay, a nuclear proton is converted into a neutron (Z#Z-1) An example of e.c. relevant to nuclear medicine is the following decay: Internal Conversion •Alternatively, the energy liberated from the isomeric transition can be delivered In each case, the decay products include a neutrino ( ) or an anti-neutrino ( ) 201 ! 201 ! ! Tl e Hg Q to an electron ejected from the atom (like Auger electrons vs. char. x-rays). Neutrinos have no charge, spin 1/2, and mass ~ 0.1 - 1 eV (?) 81 + " 80 + # + •Again, electrons rearrange to fill the vacancy left by the i.c. electron, resulting None of the products of this decay are used in imaging, rather, Beta decay is mediated by the ‘weak force’. in characteristic x-rays and/or Auger electrons. characteristic x-rays filling the vacancy are detected by gamma cameras. •Gamma emission and i.c. electron compete in the same nuclide decay. 22 May 2008 13 22 May 2008 14 22 May 2008 15 Decay Schemes Bushberg Example: 99mTc 22 May 2008 16 22 May 2008 17 22 May 2008 18 [email protected] 3 [email protected] 4.
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