AAA-Spring 20021

2 Table of nuclides Z = # of protons (A - Z) = # of neutrons Stable nuclides: Z ~ A/2 How did they get made?

AAA-Spring *****Nuclear Structure***** The only stable isotope of aluminum is Al. How many neutrons and protons are in the aluminum nucleus? How many electrons are in the neutral aluminum atom? (14 neutrons, 13 protons, 13 electrons)

AAA-Spring Table of nuclides Zn, Se, Cu, Mo, Ni, Sn

AAA-Spring Crab Nebula

AAA-Spring *****Explanation of the Crab***** The Crab Nebula, filled with mysterious filaments, is the result of a star that was seen to explode in 1054 AD. This spectacular supernova explosion was recorded by Chinese and (quite probably) Anasazi Indian astronomers. The filaments are mysterious because they appear to have less mass than expelled in the original supernova and higher speed than expected from a free explosion. In the above picture taken recently from a Very Large Telescope, the color indicates what is happening to the electrons in different parts of the Crab Nebula. Red indicates the electrons are recombining with protons to form neutral hydrogen, while blue indicates the electrons are whirling around the magnetic field of the inner nebula. In the nebula's very center lies a pulsar: a neutron star rotating, in this case, 30 times a second. (It (The Crab nebula is about 6,500 light years away.)

AAA-Spring Nuclear Decays Alpha emission –Alpha = helium nucleus = 2 protons + 2 neutrons –Z changes by 2, A by 4 Beta emission –Beta = electron or positron –Z changes by one, A stays the same Gamma emission –Gamma = photon = “particle of light” –Neither A nor Z change Neutron emission –A changes but not Z

AAA-Spring *****Some nuclear decays***** What are the daughter nuclides for the following (probably unphysical) decays? Go to table to findtable your way around. Alpha decay of B12? (B = boron) Neutron decay of O19? Beta (electron) decay of N16? (N = nitrogen) Positron decay of C11? (Li8, O18, O16, B11)

AAA-Spring n p + e - Radioactive Carbon C14 N14 + e {e - = electron} How did we get electrons in the nucleus?? p n + e +

AAA-Spring How radioactive are you? How many carbon atoms are in you? –Maybe 1 kg of you is carbon???????

AAA-Spring How radioactive are you? How many carbon atoms are in you? –6 x atoms/mole x 1 kg of carbon x (1000/12) moles/kg = 5 x carbon atoms

AAA-Spring How radioactive are you? How many carbon atoms are in you? –5 x carbon atoms How many of these are C14? –Only 1 in is C14 or 5 x C14 atoms

AAA-Spring How radioactive are you? How many carbon atoms are in you? –5 x carbon atoms How many of these are C14? –5 x C14 atoms How many of these decay each second? –About half decay in 5,000 years

AAA-Spring How radioactive are you? How many carbon atoms are in you? –5 x carbon atoms How many of these are C14? –5 x C14 atoms How many of these decay each second? –2.5 x atoms x (1/5,000 years) x (1/[3 x 10 7 seconds/year]) x 1.4 = 250 per second

AAA-Spring How radioactive are you? How many carbon atoms are in you? –5 x carbon atoms How many of these are C14? –5 x C14 atoms How many of these decay each second? –250 (or 7 x 10 9 in a year!!!) Why aren’t we all dead? Or at least glowing in the dark? Dose is < of average from all sources

AAA-Spring Radioactive decay How fast does C14 go to N14? Watch one atom –Never see decay in progress –C14 for a while, then suddenly is N14 Watch many atoms, initially all C14 –See only mixture of C14 and N14 atoms –Early on, mostly C14 –Later, mostly N14 –After very long wait, only N14 t 1 = t 2 = t 3 = T 1/2 Time for 1/2 to decay = half life –{= 5730 years for C14} C14 N14 t1t1 t2t2 t3t3 ??

AAA-Spring Simulations of N17 and O21 decays Go to the Simulation

AAA-Spring Example from Web Be-11 B-11 Be B (decay rate of Be) = (1/T m ) x (number of Be)

AAA-Spring Example from Web Be-11 B-11 Be B (decay rate of Be) = (1/T m ) x (number of Be) Curve NOT smooth Curve VERY “noisy” at long times Curve NOT same on successive runs Curve does NOT go through 1/2 at t = T 1/2

AAA-Spring *****Decay and Half-lives***** If I start with 1024 radioactive atoms that decay with a half life of ten minutes, how many are left after a half an hour? If I start with 1024 radioactive atoms and after two hours I have only 16 left, what is their half life? If I start with 1024 radioactive atoms and there are 256 left after an hour, how many will be left after two hours? If I start with 10 6 radioactive atoms and there are 10 4 left after an hour, how many will be left after two hours? After three hours? (128, 20 minutes, 32, [10 2, 1])

AAA-Spring C-14 Dating Physicist’s first (1950s) look at problem –Source of C-14 –Distribution –Organic content while alive = R 0 –Decay of C-14/C-12 ratio after death, R t –Time since death t = T 1/2 log 2 (R 0 /R t )

AAA-Spring *****C14 dating links***** Here’s a fun place to startfun place Go to this site, click on radiocarbon at the left, and explore the several topics there.Go to this site This one gives a LOT of more detailed information if you found not enough at the one above. As in the first, it may take some prowling around to find what you want.This one

AAA-Spring Upper Atmosphere—Source of C-14 Cosmic ray junk neutron N-14 proton C-14 O2O2 CO 2 Nucleus of anything Production rate: 2 atoms/second-cm kg/yr

AAA-Spring Atmospheric/oceanic mixing 2% 98%

AAA-Spring Steady state C14 concentration generation decay New C14 Lost C14 atmosphere oceans C12 and C14 Atmospheric ratio R 0 = C14/C12 = 1.2 x C14 concentration adjusts until generation rate = decay rate: gives

AAA-Spring Living organisms C12 C14 Living organisms exchange with atmosphere to give ratio R 0 = C14/C12 = 1.2 x in tissues of the organism

AAA-Spring t years after death NO CO 2 exchange with atmosphere C12 is stable C14 decays Ratio at time t is reduced to R t with R t = C14/C12 at time t = R 0 (1/2) t/T (T = T 1/2 ) = R 0 e -t/T (T = T m ) t = T 1/2 log 2 (R 0 /R t )= T m ln(R 0 /R t ) with T 1/2 = 5568 years or T m = 8033 years

AAA-Spring “Radiocarbon Age” Follow this procedure, result quoted as: radiocarbon age = t - {(date of experiment) } BP BP = “before present” “present” = 1950

AAA-Spring *****radiocarbon age***** 1) If a dating experiment is performed in the year 2000 and gives a t = 750 years, what is the “radiocarbon age”? And what is the apparent (uncalibrated) calendar age of the sample? 2) Try again, now with a dating experiment in 1975 which gave a t of 2500 years. 1) 700 years BP and 1250 years AD 2) 2475 years BP and 525 years BC

AAA-Spring FRIDAY BRAINSTORMING SESSION– WHAT MIGHT GO WRONG WITH THIS SCHEME??

AAA-Spring But how to measure R(t)?

AAA-Spring Calibration Corrections

AAA-Spring UNUSED SLIDES

AAA-Spring Nuclear stability: C-8 Carbon-8 –Too many protons –Like charges repel –Nuclear forces –Roughly, Z ~ A/2 for stability Decay scheme – 8 6 C –––> 6 4 Be + 2 p –Check numbers of p and n –Check A and Z 86C86C 6 4 Be p p

AAA-Spring Table of nuclides Z = # of protons (A - Z) = # of neutrons

AAA-Spring Nuclear stability: He-8 Helium-8 –too many neutrons –Z ~ A/2 –What’s wrong with neutrons? Only high energy n states available Lower energy states OK for p One possible decay scheme – 8 2 He –––> 7 3 Li + e - + n beta decay = electron emission Note: n –––> e - + p 8 2 He e-e- n 7 3 Li

AAA-Spring Table of nuclides Z = # of protons (A - Z) = # of neutrons

AAA-Spring A Beryllium/Boron Clock Many different kind of clocks based on radioactive decay To measure 30 seconds: –Bucket of Be11 at t = 0 –Ring buzzer when ratio Be/B ~1/3 Ratio of Be/B tells elapsed time since started with full bucket of Be Variation among clocks: mostly “what starts the clock?”