Radioactive Dating

1. Radioactive Dating Lecture Sixteen, Feb. 21, 2003

2. Last Time: Distance to nearest star • Was a very long quest. Finally we were able to measure the parallax of nearby stars such as Alpha Centuri. Very distant star Nearby star Earth’s orbit

4. Cepheid Variable Stars • Oscillate with a regular period. Intrinsic brightness of star is proportional to its period. • Measure the period of the variable star and its apparent brightness and infer the stars actual distance. • Need to calibrate the relation with Cepheids at known distances. • Finally, Hubble telescope can resolve individual Cepheid variable stars at cosmological distances.

5. Hubble resolves Cepheids in M100 Allows accurate determination of distance Spiral galaxy M100

6. Hubble’s Law Gives Expansion Rate of Universe • Distant galaxies are moving away with velocity v=Hd • Easy to measure velocity v from redshift of spectral lines. • Distance d was very hard! • Hubble constant is now H=v/d. • Distance divided by velocity is a time: d/v=T=1/H= Age of Universe! • Age of Universe 13 B. years follows form 1/H.

7. Timeline • Big bang. • Creation of galaxies and first stars. • Creation of chemical elements. • Creation of solar system: Sun, earth and planets. • Origin of life on Earth. • Evolution and mass extinctions.

8. Radioactive dating • Measure present amount of a radioactive isotope. • Have some way to infer the initial amount. • Compare the decrease to the known rate of radioactive decay to infer an age. • Rate of radioactive decay of an isotope characterized by its half life. • Example 14C has a half life of about 5000 years. • After 5000 years half of the original 14C is gone and after 10,000 years ¾ of original amount has decayed. • Note, need to chose an isotope with a half life comparable to the age you are trying to measure. • Cant use 14C to measure 4.6 Billion year age of earth.

9. Radioactivity, a Tour • * DANGER - SEVERE RADIATION * ENTER AT YOUR OWN RISK * Enjoy Your VisitOur Safety Inspector Homer Simpson will now take you on a tour of the Springfield Nuclear Power Plant.

11. Can you feel it? That tingling in your bones? Well, yes, that's partly because of the radiation, but mainly it's because you're in Burns territory now! The Springfield Nuclear Power Plant dominates the landscape here, from its main office to its giant turbines to the cut-off valve that I once plugged with my ample frame, thus averting a nuclear meltdown.And then there's the fuel rod and nuclear waste storage areas. Is it me, or does the Springfield Isotopes baseball field (property of C. Montgomery Burns) seem to be just a bit too green?

12. Radioactivity a Primer • Atoms have an electron cloud around a nucleus which is made of protons and neutrons. • A free neutron decays with a half-life of 10.6 minutes into a proton (p) an electron (e) and an antineutrino (). n! p + e- +  • Protons and electrons have opposite charges while neutron and antineutrino are uncharged. Electric charge is conserved in all reactions. Initial charge = 0 = Final charge = +1 + -1 + 0

13. Half-Life • Nuclear reactions are probabilistic. A given nucleus could decay instantly or it could survive for the age of the Universe. • The half-life is the amount of time one has to wait until the probability of decay is 50%. • If you start with 8lbs of radioactive material. After one half-life 4lbs remain, after two half-lives 2lbs remain and after 3 half-lives only one lb is left. Thus only ¼ of the initial # of neutrons will be left after 20 minutes because the neutron half-life is 10 minutes.

14. Antiparticles • According to relativity, every particle has an antiparticle with the same mass but opposite electric charge. • When particles and antiparticles meet they annihilate into gamma rays. • Example, the anti-electron is known as a positron (e+) and has a positive charge but the electron’s mass. [The proton is 2000 times more massive than an electron.] • Antihydrogen is an atom made from a positron and an anti-proton. It is the simplest atom of antimatter. • Science Fiction writers have speculated that antimatter would make a very efficient rocket fuel.

15. Radiocarbon dating • Carbon 14 (14C) is an isotope of carbon with 6 protons and 8 neutrons in the nucleus. One of these bound neutrons decays with a half-life of 5000 years converting 14C!14N + e- +  • With a half-life of only 5000 years, almost all of the primordial 14C has long since decayed. • However, a very small amount of 14C is continually being made by cosmic rays interacting with the earth’s atmosphere.

16. Dating old wood • While a tree is alive it continually exchanges carbon with the atmosphere. This replenishes the very small amount of 14C present in the tree. • However, when the tree dies it stops exchanging C with the atmosphere. With no new source, the amount of 14C slowly decays. • One can date old pieces of wood by measuring how much 14C is left. The smaller the amount, the older the wood. • Very useful in archeology! • However, can’t measure ages much longer than 5000 year half-life.

17. Radioactive Dating of Rocks • To measure the billions of year ages or rocks need to use isotopes with longer half-lives. • Potassium 40 (40K) is an isotope with 19 protons and 21 neutrons. It decays to Argon 40 with a half-life of 1.28 billion years. • Uranium 238 has a half-life of 4.47 billion years. • The radioactive decay of 40K and 238U are important sources of heat for the earth and help drive plate tectonics.

18. Potassium Argon Dating of Rocks • If the produced Argon (a noble gas) can not escape from the middle of a solid rock then, carefully measure the ratio of 40Ar to 40K in a rock. The larger the ratio the older the rock since K is turning into Ar slowly. • Note, if the rock is melted (for example from the heat of a nearby asteroid impact) then the Argon gas will escape. This “resets” the K to Ar clock. • You are measuring the time since the rock was last melted.

19. Dating the earth • Problem: we have not found any rocks as old as the earth. All of the earth rocks we have been able to study have been melted at some time in their past. Thus the oldest known earth rocks are about 3.5 billion years. • We can not directly radioactively date the earth!

20. Meteorites • Meteorites in general are small asteroids that have fallen to earth. • Asteroids formed at the same time as the rest of the solar system. Thus we think all of the planets, the sun, and the asteroids and comets all have the same age. • Asteroids have circled the sun almost undisturbed for the life of the solar system. They have not been remelted. • The radioactive age of most meteorites is 4.6 billion years. Thus we think the earth and sun are 4.6 billion years old because this is the age of the meteorites.

21. Asteroids fall as Meteorites

23. Radioactive Dating of Oldest Stars • This is a new way to get the age of the universe. • Find a star that you think is very old. Spectrum shows very few Fe lines. Chemical elements except H, He made in stars. Very old star has few heavy elements. • Measure abundance of Thorium and Uranium from strength of spectral lines. Note, Uranium lines are very faint and hard to observe. • Need very high quality spectra from long exposures at the largest telescopes. • Asume ratio of original U to Th was the same as the original ratio in the sun. • Infer the age of the star from the amount of U that remains.

24. Independent Age of Universe • We have found stars with radioactive ages near 12 § 3 billion years. • We think these formed within 1 billion years of the big bang. • This gives a direct age to the universe that is independent of (but consistent with) the “expansion age” from the rate of the expansion of the universe.

25. Nuclear Power For Spacecraft • Needed for last third of this class to explore the outer solar system. • “Nuclear Batteries” have radioactive isotopes, usually Plutonium, that decay and produce heat. This heat is turned into electric power. • Cassini Mission to Saturn uses nuclear batteries because it is very far from the sun so solar cells are inefficient. • Concern that launch accident may spread plutonium.

28. Nuclear Rockets • One can use a nuclear reactor to heat hydrogen gas to very high temperatures and produce a rocket exhaust. • Conventional chemical rocket carries both H and O (note O is heavy) to burn to make H2O. • Nuclear rocket does not need O and can get the H hotter and thus moving faster.

30. Nuclear Explosive Power • Explode a whole series of small nuclear weapons behind a pusher plate. • Very high temperatures reached in nuclear explosions accelerate debris to very high speeds. • This makes an incredibly powerful rocket if your spacecraft survives.

32. Small Scale Test with Conventional High Explosives in 1950s • Orion project to build powerful spacecraft that could take large payloads anywhere in the solar system. • Test of model (about 1 meter in size) with conventional ~1kg explosive charges.