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• Slide 1
• and decays, Radiation Therapies and Diagnostic, Fusion and Fission This Lecture: Radioactivity, Nuclear decay Radiation damage, radiation therapies and diagnostic Evaluations for Prof. T. Montaruli today Previous lecture: nuclear physics
• Slide 2
• Final Exam Fri, Dec 21, at 7:45-9:45 am in Ch 2103 About 40% on new material 2 sheets allowed (HAND WRITTEN!) The rest on previous materials covered by MTE1 MTE2 MTE3.
• Slide 3
• New material not covered by MTE1,2,3 Ch 40.4-5 particle in a box: wave functions, energy levels, photon absorption and emission, 40.10 tunneling Ch 41.1-3 H-atom quantum numbers and their meaning, wave functions and probabilities, electron spin Ch 41.4-6 Pauli exclusion principle, multi-electron atoms, periodic table, emission and absorption spectra Ch 41.8 Stimulated emission and Lasers Ch 42.1-3 Nuclear structure, atomic mass, isotopes, binding energy, the strong force Ch 42.5 Radioactivity, Ch 42.6 Nuclear decay, Ch 42.7 Biological applications
• Slide 4
• Women Nobel Prizes The only 2 female Nobel Prizes in Nuclear Physics! Maria Goeppert-Mayer 1963 Shell Model of Nucleus 1903 Marie Curie (with Pierre) in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel
• Slide 5
• 5 Nuclear Physics Strong force: attractive force keeping p and n in nucleus (short range) It is convenient to use atomic mass units to express masses 1 u = 1.660 539 x 10 -27 kg mass of one atom of 12 C = 12 u Mass can also be expressed in MeV/c 2 From rest energy of a particle E R = mc 2 1 u = 931.494 MeV/c 2 Binding energy: m nucleus < Zm p + (A-Z)m n = Zm p + Nm n The energy you would need to supply to disassemble the nucleus into nucleons E binding = (Zm p +Nm n -m nucleus )c 2 = (Zm p +Zm e +Nm n + -Zm e -m nucleus )c 2 =(Zm H + Nm n - m atom ) c 2 5 C 12 6
• Slide 6
• 6 Fission and Fusion
• Slide 7
• Stable and Unstable Isotopes Isotope = same Z Isotone = same N Isobar = same A
• Slide 8
• Stability of nuclei Dots: naturally occurring isotopes. Blue shaded region: isotopes created in the laboratory. Light nuclei are most stable if N=Z Heavy nuclei are most stable if N>Z As # of p increases more neutrons are needed to keep nucleus stable No nuclei are stable for Z>83
• Slide 9
• Radioactivity Discovered by Becquerel in 1896 spontaneous emission of radiation as result of decay or disintegration of unstable nuclei Unstable nuclei can decay by emitting some form of energy Three different types of decay observed: Alpha decay emission of 4 He nuclei (2p+2n) Beta decay electrons and its anti-particle (positron) Gamma decay high energy photons
• Slide 10
• Penetrating power of radiation Alpha radiation barely penetrate a piece of paper (but dangerous!) Beta radiation can penetrate a few mm of Al Gamma radiation can penetrate several cm of lead
• Slide 11
• Slide 12
• The Decay Rate probability that a nucleus decays during t number of decays (decrease)= NxProb=rNt N=number of independent nuclei Constant of proportionality = decay rate (in s -1 ) The number of decays per second is the activity # radioactive nuclei at time t # rad. nuclei at t=0 time constant
• Slide 13
• The half-life After some amount of time, half the radioactive nuclei will have decayed, and activity decreases by a factor of two. This time is the half-life
• Slide 14
• Units The unit of activity, R, is the curie (Ci) The SI unit of activity is the becquerel (Bq) Therefore, 1 Ci = 3.7 x 10 10 Bq The most commonly used units of activity are the millicurie and the microcurie
• Slide 15
• An Example 232 Th has a half-life of 14 x10 9 yr Sample initially contains: N 0 = 10 6 232 Th atoms Every 14 billion years, the number of 232 Th nuclei goes down by a factor of two. N0N0 N 0 /2 N 0 /4 N 0 /8
• Slide 16
• Radiocarbon dating 14 C (Z=6) has a half-life of 5,730 years, continually decaying back into 14 N (Z=7). In atmosphere very small amount! 1 nucleus of 14 C each 10 12 nuclei of 12 C If material alive, atmospheric carbon mix ingested (as CO 2 ), ratio stays constant. After death, no exchange with atmosphere. Ratio changes as 14 C decays So can determine time since the plant or animal died (stopped exchanging 14 C with the atmosphere) if not older than 60000 yr
• Slide 17
• Carbon dating A fossil bone is found to contain 1/8 as much 14 C as the bone of a living animal. Using T 1/2 =5,730 yrs, what is the approximate age of the fossil? A.7,640 yrs B.17,190 yrs C.22,900 yrs D.45,840 yrs Factor of 8 reduction in 14 C corresponds to three half-lives. So age is 5,730 x 3 =17,190 yrs
• Slide 18
• Heavy nucleus spontaneously emits alpha particle Decay processes: = 4 He nucleus loses 2 neutrons and 2 protons. It becomes a different element (Z is changed) Example: 92 protons 146 neutrons 90 protons 144 neutrons 2 protons 2 neutrons Alpha particle
• Slide 19
• A quantum process This is a quantum-mechanical process It has some probability for occurring. For every second of time, there is a probability that the nucleus will decay by emitting an - particle. This probability depends on the width of the barrier The -particle quantum-mechanically tunnels out of the nucleus even if energy is not > energy barrier Potential energy of in the daughter nucleus vs distance Coulomb repulsion dominates Nuclear attraction dominates
• Slide 20
• Disintegration Energy In decays energy-momentum must be conserved The disintegration energy appears in the form of kinetic energy of products M X c 2 = M Y c 2 + K Y + M c 2 + K E K Y K = (M x M y M )c 2 Textbook: neglect K Y since M