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

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2t1/

2 is

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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