# Age dating of rocks by radiometric method. Radioactive decay and half-life Parent nucleus changes or decays into daughter nucleus by: - Emitting an electron.

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Age dating of rocks by radiometric method

Radioactive decay and half-life Parent nucleus changes or decays into daughter nucleus by: - Emitting an electron (Beta decay) - Emitting an alpha particle (He nucleus) - Capturing an electron Half life is time it takes for 1/2 of the original parent nuclei to decay to the daughter nuclei. So, after: - 1 half life --> 1/2 as much parent - 2 half lives-->1/2 of 1/2 = 1/4 as much parent - 3 half lives-->1/2 of 1/4 = 1/8 as much parent - and so on. This is the basis for radiometric age dating.

We can write a simple formula for how much parent is left t years after the rock formed: N P (t) = N P (t=0)x(1/2 t/t(1/2) ) and how much daughter grows after t: N D (t) = N D (t=0) + [N P (t=0) - N P (t)] If we can find these Ns, we can solve these relationships to find t = age of the rock. Mathematics raises its ugly head!

Beta decay Electron capture Alpha decay

Problems with this method…and the solution To apply the formula, three conditions must be met: -Absence of original daughter (really, knowledge of how much originally present) -Maintenance of a closed system -Constancy of radioactive decay rates Solve first two by clever method of isochrones Constancy of t 1/2 -Never observed to vary; no way to change in lab -Consistency of data fitting isochrone method

*Rb 87 *Sr 87 0 2468 0 3 6 9 original Isochrone method of radiometric age-dating Note: * means normalized by Sr86. t 1/2 isochrone 2t 1/2 isochrone t 1/2 2 t 1/2 t 1/2 2 t 1/2 t 1/2 2 t 1/2

MethodAge (B yrs) Uranium-Lead3.81 +/- 0.02 Rubidium-Strontium3.71 +/- 0.07 Samarium-Neodymium3.75 +/- 0.04 Lead-Lead3.70 +/- 0.07 Age of rocks from Isua, Greenland

Ages of meteorites, Earth, Moon (Billions of years) Meteorites (primitive):4.55 +/- 0.01 Oldest Earth rocks--Yilgarn Zircon from W. Australia4.404 +/- 0.08 Rocks from Lunar Highlands4.47 +/- 0.1 Conclusion: Age of Earth and Solar System about4.5 Billion Yrs

Carbon-14 dating

C 14 age dating - Ratio of C 14 /C 12 ~ 10 -12 in Earths atmosphere and all living things - C 14 decays & is replaced --> equilibrium -After death, C 14 is not replaced, so C 14 /C 12 decreases, with -Halflife = 5730 yrs -Dont need isochrone analysis because we know C 14 /C 12 at t=0 - Accurate to ~ 70,000 years

Curve of knowns from 1949

The world of particle physics An incomplete introduction

Atomic and nuclear physics and quantum mechanics 1st third to half of 20th Century Then attention turned to understanding the nucleus As technology improved --> more & more complex picture emerged: particle zoo Around 60s a theoretical picture developed to make sense of the mess Particle physicists today trying to go even deeper: can we calculate everything from first principles?

The Atom Made of: Protons, Neutrons, Electrons Held together by electromagnetic force Bohr & others: simple picture + quantum assumptions Schrodinger/Heisenberg: non-relativistic mathematical framework Dirac: extended to include relativity His work taken to high degree of sophistication by Feynmann, Schwinger, Tomanaga-->Quantum Electrodynamics or QED

QED phenomenally successful Example: QED calculation of magnetic moment of electron gives: –2.00231930435 and –Experiments confirm this number! Treats electron as a point particle Not quite what wed like…still have to put in mass & charge of electron Note: QED does not work as well for protons…they are NOT points

Forces mediated by virtual particles! Photons carry the interaction between charged particles –Think of medicine ball analogy But…these are virtual photons: they pop up out of the vacuum (=nothing) –Their energy is temporarily borrowed –Heisenberg: Ex t = (h/2 ) h-bar –The higher is E, the less time you get to keep it –Range of interaction no more than c t

What about the nucleus? Probe by shooting particles at it Very small, all the mass: what holds it together? –Because positive protons repel each other –Strong or nuclear force: has to be strong, observed to be short ranged –This is why only see fusion in stellar cores In 1930s, Yukawa developed theory or picture of strong force mediated by virtual mesons (pions)

Yukawas explanation Force mediated by a virtual particle Calculated its properties: mass is in between proton and electron--> mesos Still quite massive, so from Ex t = (h/2 ), the range is short and fits measurements for Strong Force Using radioactive elements and cosmic rays as sources, physicists began searching for the meson

Meanwhile, back at Nuclear Ranch… Science knew about 3 forces: –Gravity - Electromagnetic - Strong Nature of Beta decay made it clear that there was a fourth force: Weak Beta decay leads to a transformation –Neutron -> Proton + electron (plus neutrino) –I.e. Weak force didnt push/pull, but it was still an important interaction Its virtual carrier: W particle –Very massive ~ 80 x proton –So interaction quite improbable or weak

The neutrino Going right along with the Weak Force was a new particle: the neutrino –Massless*, charge = 0 –Interacts only via the Weak Force Postulated (required) to conserve energy and momentum in Beta decay, but not discovered until 1956 –100 Billion/sec/cm 2 is continuous flux! –Weak force, neutrinos critical to nuclear fusion in stellar cores * Note that neutrinos are now thought to have a small, but finite mass.

Particle zoo gets populated Accelerators reach higher & higher E From Einstein: E = mc 2, we expect that more massive particles will now be found –More massive and/or more tightly bound And they come…pions, kaons, rhos, muons, and on-and-ons Their lifetimes are by and large agonizingly short –But they are real and must be explained

A taxonomy grows In analogy to Mendeleevs construction of the periodic table well before atomic physics understood –Physicists begin to group into categories Particles started to turn up that could only be explained or categorized if a new Quantum Number introduced: Strangeness –Driven by appearance of the V or Strange particles

Categories Strong (Hadrons)/Not Strong (Leptons) Strange/Not Strange Fermions/Bosons Doublets, Triplets, Quadriplets,…on to Octets, Decipets. 100s of particles discovered by 50s/60s We need a knight on a white horse!

Enter Murray Gell-Mann! He says (less than 1/2 seriously): what if the protons, neutrons and other hadrons are composed of smaller, more fundamental particles? Called them Quarks And assigned Quantum Numbers to them, including fractional electric charges: 1/3, 2/3, -1/3, and masses roughly 1/3 proton mass

Quantum Chromodynamics = QCD

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