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)
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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 X ~1500 nuclides exist A (atomic mass number) = Z + N Z X N Z 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] [*] A • Alpha particle always carries Q energy as kinetic energy (monoenergetic) Z X Z X + 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) N t = N 2 T1 / 2 ( ) 0 22 May 2008 10 22 May 2008 11 22 May 2008 12