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Date Created: 10/21/15
OCEANOGRAPHY 640 LECTURE OUTLINE 0N RADIOACTIVE DECAY Radioactive decay is a spontaneous Nuclear Transformation or change in the chemical identify of an original parent atom to a different element daughter During the transformation the energy configuration of the nucleus changes to a more stable state and particles and energy are emitted from the original nucleus The nuclear decay process is characterized by a specific decay period half life and decay energy The half life is the time required for one half the atoms in a sample to decay Because the decay is an event that happens atom by atom and generally without regard to temperature pressure or chemical environment the progress is described in terms of number of atoms N rather than in moles or mass Half lives vary from fractions of a second to millions of years Very short half lives are difficult to measure and those lt 103918 seconds are considered instantaneous Half lives gt 1015 years often cannot be measured above normal background because the total activity is so low In radioactive decay there is a transition from a definite quantum state of a parent to a definite quantum state of its daughter The energy difference is equal to the decay energy which is the sum of the electromagnetic radiation plus kinetic energy imparted to the resulting masses Types of Decay Alpha 0c Beta 5 Gamma y In alpha decay the nucleus emits an alpha particle which is the same as a helium nucleus 2 neutrons plus 2 protons with a charge of 2 Alpha particles are large and heavy compared to most subnuclear particles and interact strongly with other matter They are not able to penetrate even through paper in many cases In 5 decay the process involves creation or emission of either electrons or positrons or capture of an electron The energy of l decay is represented by the maximum energy because each decay is accompanied by a neutrino of minute but varying mass and no charge This combination makes the decay energy spectrum wide and disperse with only the maximum energy at a de nitive level Gamma decay is emission of electromagnetic radiation transition between energy levels of the same nucleus or internal conversion nuclear eld interacts with orbital electron It does not represent a transformation from one element to another just a change in energy level of the original nucleus Spontaneous ssion occurs when the nucleus splits into two roughly equal parts this process releases electromagnetic radiation neutrons and large fragments of nuclei Emission of alpha or beta particles changes the atomic number of the nucleus by 2 or 1 units respectively as shown in the gure below place Figure 1 here Equations of Radioactive Decay and Growth Decay half life is represented b the exponential decay equation N Noe m where N the number of atoms present at any time N0 the number of atoms present at t0 t the elapsed time since t0 7t decay constant speci c to the particular nuclide Place Figure 2 here decay ole growth of N2 The rate of change of N1 with time dN 1 LlNl dt where M the decay constant in units of lt eg min39l and solving gives N1 Nloe39M 0 for one half life t 2 by de nition g N1 11 and N e1 2 ekt122 All2 0693 0693 t l1 and1 tm The activity of a radionucline AN is an expression of the amount present and is given in units of decays per unit time Growth of Radioactive Daughters N tl N27t2 where N1 parent isotope N2 daughter isotope 7L1 decay constant for N1 7L2 decay constant for N2 N2 value of N2 at t0 N2 JI Nf Mt e N3 eth A 21 Activity AN a measure of the amount of N present Example Growth of Radioactive Products dN 2 lel 7N2 7L2 dt N20 value of N2 at t0 11 0 V111 411 0 wilt 1N1e e N2e 1 Example AN7t N2 Calculate activity NA for 1 lug 238U halflife 4468 x 109 g 1 x 10 396 2 U 253 x1015 atoms N X 602 X 1023 atomsmole 0693 0693 1 A T 9x 5m1nyr t 4468 x10 y 525 x10 296 x 103916 min391 NA for 1 pg 238U 0749 dpm dps bq becquerel Speci c Activity Nkwt concentration dpm gm Parent Daughter Relationship Based on relative length of half lives 1 Parent tl2 ltlt Daughter 2 Parent t 10X D11 3 Parent tl2 gtgt Daughter Place Figure 3 here Figure 3 The case of no equilibrium a total activity b activity due to parent 112 080 hr c extrapolation of nal decay curve to time zero d daughter activity in initially pure parent Place Figure 4 here Figure 4 Transient equilibrium a total activity of an initially pure parent fraction b activity due to parent 112 080 hr c decay of freshly isolated daughter fraction 112 080 hr d daughter activity in freshly puri ed parent fraction e 7 daughter activity in parentplus daughter fractions Place Figure 5 here Figure 5 Secular equilibrium a total activity of an initially pure parent fraction b activity due to parent tlz oc this is also the total daughter activity in parentplusdaughter fractions c decay of freshly isolated daughter fraction tlz 080 hr d daughter activity growing in freshly puri ed parent fraction Homework luggBSU 45 x 109y 234Th 241 d How many ug 234th to have secular equilibrium with the U Place Figure 6 here Figure 6 Depth pro les of temperature nitrate pigments and 234Th in the eastern Paci c Ocean from Coale and Bruland 1987 N1 for 234Th actiVit ratio NA for U y N14 1 at secular equilibrium N2 N1X1Nz 7L2 N37L3 N 7L Place Figure 7 here Figure 7 Portions of the uranium and thorium radioactive decay series The radiogenic Th isotopes discussed in this paper are indicated by the boxes Alpha decays are designated by vertical arrows beta decays by diagonal ones Place Figure 8 here Figure 8 Schematic diagram depicting probable disequilibrium relationships of 238Useries nuclides with respect to 230Th in deepsea sediments D s 1co a z az Steady State Place Figure 9 here Place Figure 10 here Figure 10 Typical 226Ra and 228Ra pro les from the western basin of the North Atlantic collected during TTONAS Table 1 North Atlantic Surface Water Natural Radioactivity Fallout Radioactivity 40K 320 pcil 3H L8 3174 pC 87Rb 29 1370s 021 038 234U 13 90Sr 013 025 238U 12 14C 00201 04 3H 063 2391311 0000300012 14C 0160 18 l p Ci l pico Curie 103912 Ci 1 Ci 37 X 1010 disintegration per second 1 Bq l Becquerel l dps Place Figure 11 here Schematic diagram showing oceanic cycles of selected members of the U and Th Figure 11 Solid horizontal arrows correspond to radioactive decay characterized by a rate decay series constant Solid vertical arrows denote uxes across the sedimentwater interface and wavy vertical arrows represent removal from the atmosphere for 21OPb or oceans through chemical scavenging and particle settling after Cochran 1980a Place Figure 12 here Figure 12 Simple box model for describing U and Thseries disequilibrium The subscripts P and D denote the parent and daughter for a radioactive parent decaying to a reactive radioactive daughter N refers to the number of atoms 7 is the radioactive decay constant and k is the first order rate constant for processes other than radioactive decay for example chemical scavenging The reciprocal of k is E the mean residence time of the daughter in the box to non decay removal Place Figure 13 here 228 Figure 13 Plot of Ra against depth in the water column in the North Atlantic The solid circles represent samples collected in 1970 at the second GEOSECS intercalibration station Trier et al 1972 Open circles correspond to a nearby station sampled in 1981 during the TTO project Key et al 1985a Place Figure 14 here Figure 14 Dissolved 22an activity as a function of depth near the bottom The profile is from GEOSECS station 263 Pacific Ocean and the 22an excess relative to 226Ra near the bottom is caused by Rn diffusing out of sediments after Sarmiento et al 1976 Place Figure 15 here Figure 15 Dissolved 22an activity as a function of depth in the surface ocean The profile was taken at GEOSECS station 263 in the tropical Pacific Ocean The temperature and 226Radepth profiles are indicated by the solid line The 22an deficiency relative to 226Ra in the upper 50 m is caused by loss at the atmosphere Place Figure 16 here Figure 16 Plot of the mean 3H content of rain at Valencia Ireland from 1952 to 1974 solid circles Also given is the total annual northern hemisphere 90r deposition open circles From this comparison it is clear that the time history of the input of these two isotopes is quite similar The differences are related to the ratio of escaping neutrons producing 3H to uranium fissions producing QOSr for the various bombs tested This diagram was published by Dreisigacker and Roether Place Figure 17 here Figure 17 Records of QOSr concentration as a function of time in surface waters as reconstructed through measurements on growthringringdated corals These results were obtained by Toggweiler of LamontDoherty Earth Observatory as part of his PhD thesis research
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