Lecture 7: Time
Today we Do Geology!!

Absolute vs Relative
--Relative says one thing happenned before the other, but little else.
--Led to great debates about the age of the Earth
--Absolute gives definite ages in terms of years
--Quantifies how long ago.

Relative Ages

Laws of original horizontality and stratigraphic superposition
-Sed rx get deposited flat and the oldest stuff is on the bottom.

Unconformity -- a substantial break in the stratigraphic record.
--Implies a substantial period of erosion or non-deposition.
-- a period of time not "recorded"
angular unconformity -- angular discontinuity -- flat rx on tilted rx
--implies period of deformation, erosion, further deposition
--this indicates quite a lot of "missing" time.

Use Grand Canyon Example How to interpret?

Rock Correlation
Want to know what happened in Earth history in widely different locations.
1) Rock correlation -- hook up rocks that look alike
--The key bed -- aparticular strata that is very distinctive
2) Fossil correlation -- hooks up rocks that formed at the same time
--The index fossil
-- common occurrence
-- wide geographic distribution
--very restricted age range

The musical group analogy
The Grateful Dead -- not an index fossil
The Sex Pistols -- a very good index fossil -- 1978-1979

Why is this important?
--Remember the facies model -- not all rocks being deposited at once are similar,
--and similar rocks may be deposited over a time span, though not necessarily in the same place.
-- remember barrier islands and deltas

--In time sense, a sandstone may correlate with a shale, not the sandstone that underlies the shale.

Rock-stratigraphic unit -- refers to distinctive physical properties, regardless of age.
Basic unit is te formation, which is what we map in the field
these can be broken up into bigger or smaller units

Time-stratigraphic unit refers to all the rocks, regardless of physical appearence, that were deposited during the same interval of time.
Basic unit is the System -- refers to rocks deposited during a time unit sufficiently great to be used all over the wold.

Both of the above refer to rocks

We also have time units, which have nothing to do with rocks.
Basic unit is the period, which is the time during which a system of rocks were deposited.
These periods are now recognized world-wide and span tens of millions of years.

The Geologic Time Scale
UC Berkeley has an excellent Web page devoted to geologic time. Check it out!
Recognition of time periods led to the development of the Geologic Time Scale
[Use overhead]
Periods are grouped into Eras which are grouped into Eons.
Periods are split into Epochs.

Names come from Geographic locations, or surrounding feature, or Greek.
Memorize Geologic Time Scale.
--Correct spelling
--Dates to two significant figures.

Precambrian -- metamorphic and plutonic rocks
-- very few fossils
-- very primitive life forms

Paleozoic -- ancient life
--marine organisms
-- primitive fish and amphibians

Mesozoic -- middle life
--age of the dinosaurs
--Jurassic period of Jurassic Park fame

Cenozoic -- recent life
--age of the mammles, birds

Where do the numbers come from?
From Radiometric Dating!

This is an incredibally long time.
In fact, it is about the amount our National Debt. has grown since the Reagan years. Thank you Ron.

Back to nuclear physics.

Remember that an isotope refers to atome of the same element with different numbers of neutrons.
Isotopes have the same atomic number (number of protons),
but different mass number (protons + neutrons) by which they are identified (12C has 6 protons + 6 neutrons)

Radio-active Decay refers to spontaneous changes to the nuclear makeup of certain isotopes of certain elements.

What happens?
Proton + electron (Beta) = neutron.
If a neutron breaks up and emits a Beta particle,
protons increase by one and neutrons, of course, decrease by one.
Draw picture of 14C (6 protons + 8 neutrons) deecaying to 14N (7 protons + 7 neutrons)
12C is the most common isotope of Carbon.
By analogy, 40K (atomic # 19) decays to 40Ar (A.N. 18). How many neutrons -- 21 and 22.
The Parent refers to the element which is decaying.
The Daughter refers to the element which is being made.

This process of decay occurs to random atoms
and takes place at a rate that is proportional to the amount of parent atom present.
Thus, this rate is not constant.
Analogies: Babies produced depends on amount of mothers, not constant 100/year.
Intrest in bank account depends on how much money in the bank, not constant $100/year.
It acts as a percent, not a constant amount.

-dN/dt=l N

--negative because the number of N is decreasing
--Where lamda = a proportionality constant that is inversely proportional to T1/2(=0.693/l)
-- the likelihood that a decay will take place in a given amount of time; units of 1/t.

solve using calculus (-dN/N=ldt; integrate, -lnN=lt+C; etc...)

N=Noe-lt

Where No = number of parents present at the beginning

This is how the 14C method works;
we know
1) the amount of 14C (No) in the atmosphere, (produced by cosmic rays, i.e., 14N gains a beta paticle to produce 14C).
2) the decay constant of 14C

Other notes about radiometric dating

When t=T1/.2 , N = 1/2No
Half lives of some common radionuclides
14C -- 5730 years 100-70,000 years
40K -- 1.3 billion years 50,000- 4.6 billion
87Rb -- 47 billion years 10 million - 4.6 billion
others given in the bookcomputer program

Radioactive decay is a Random Process

Extra

What the Skinner and Porter book did differently

they made an apporoximation:

(1-l)^t ~= e^-lt

This is true as l goes to zero, or for isotopes with long half lives.

Then they defined the time variable as being measured in number of half lives, and l as being the proportion (rather than the probablility of the number) of parents to decay during each half life. This causes l to always be 0.5. Their method works, but the method explained above is the one that you will see if you ever read about this stuff anywhere else, or if you ever investigate population dynamics or interest rates.