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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 muchparent is left t years after the rock formed:
NP(t) = NP(t=0)x(1/2t/t(1/2))
and how much daughter grows after t:
ND(t) = ND(t=0) + [NP(t=0) - NP(t)]
If we can find these N’s, we can solve theserelationships to find t = age of the rock.
Mathematics raises its ugly head!
Beta decay
Electron capture
Alpha decay
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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 t1/2- Never observed to vary; no way to change in lab- Consistency of data fitting isochrone method
*Rb87
*Sr87
0 2 4 6 80
3
6
9
*Sr87
original
Isochrone method of radiometric age-dating
Note: * means normalized by Sr86.
t 1/2 iso
chrone
2t1/
2 is
ochr
one
t1/2
2t1/2
t1/2
2t1/2
t1/2
t1/2
2t1/2
2t1/2
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Method Age (B yrs)
Rubidium-Strontium 4.51
Argon-Argon 4.38 & 4.43
Samarium-Neodymium
4.55
Lead-Lead (internal) 4.543
Lead-Lead (whole rock)
4.549,4.555,4.551
Ages for Severin Meteorite
Method Age (B yrs)
Uranium-Lead 3.81 +/- 0.02
Rubidium-Strontium 3.71 +/- 0.07
Samarium-Neodymium
3.75 +/- 0.04
Lead-Lead 3.70 +/- 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. Australia 4.404 +/- 0.08• Rocks from Lunar Highlands 4.47 +/- 0.1
• Conclusion: Age of Earth andSolar System about 4.5 Billion Yrs
Carbon-14 dating
C14 age dating
- Ratio of C14/C12 ~ 10-12
in Earth’s atmosphere and all living things
- C14 decays & is replaced --> equilibrium
-After death, C14 is not replaced, so C14/C12
decreases, with
-Halflife = 5730 yrs
-Don’t need isochrone analysis because we know C14/C12 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 we’d 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: Ext = (h/2) “h-bar”– The higher is E, the less time you get
to keep it– Range of interaction no more than ct
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)
Yukawa’s explanation
• Force mediated by a virtual particle• Calculated its properties: mass is in
between proton and electron--> “mesos”
• Still quite massive, so from Ext = (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 didn’t 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/cm2 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 = mc2, 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 Mendeleev’s 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
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Quantum Chromodynamics = QCD