Numerical Time & Dating Methods

Numerical Time

Numerical time is the other part of the geological time scale.
It's sometimes called "absolute time," but geologic time is often measured from rocks and has errors associated with measurement.
Typically reported in millions or billions of years.
Abbreviations include Ma, Ga, mya, bya, etc.

Relative vs. Numeric Dating

Relative dating places events in sequential order and relies on stratigraphic principles, not on knowing numerical dates.
Numerical dating gives an age in units (years), and specific events are dated, usually using radioactive decay of various isotopes.

Ages of Rocks

Scientists have dated many rocks using both relative and numeric methods.
Older rocks are more rare due to destruction by plate tectonics and erosion.

Numerical Dating Methods

Dendrochronology (also sclerochronology)
Varves
Radiometric (radioisotopic) dating

Dendrochronology

Dendrochronology involves counting tree rings.
Each year of growth, most trees add a light ring and a dark ring.
Years with good growing conditions produce wider rings.
Matching tree ring patterns in living trees to deadwood (buried or in artifacts) can extend dates into the past.

Sclerochronology

Sclerochronology studies growth bands in the skeletal tissues of various organisms.
"Ming" or Hafrún the clam (~1499-2006) is an example of using sclerochronology.
- It is the oldest precisely dated non-colonial organism.
- The clam died for science.

Varves

Varves are annual couplets (light and dark band).
They form in various settings/materials:
- Coarse/fine sediments in lakes
- Calcite/gypsum in evaporating seas
- Clean/dirty in glacial ice

Radiometric Dating

Based on radioactivity: spontaneous breaking apart (decay) of atomic nuclei.
Parent (unstable isotope) decays into a daughter isotope.

Radiometric Dating - Atomic Structure

The nucleus of an atom contains protons ( $+$ ) and neutrons (neutral).
Electrons ( $-$ ) orbit the nucleus.
Atomic number = number of protons in the nucleus.
Mass number = number of protons + neutrons.

Isotopes

Isotopes are variants of the same parent element.
Atoms of each isotope have a different number of neutrons, resulting in the same atomic number but a different mass number.

Isotopes Stability

Some isotopes are stable (no decay).
Unstable isotopes decay, and the rate of decay can be measured.

Half-Life

The half-life is the time it takes for one half of the radioactive nuclei to decay.
Requires a closed system (no escape of parent or daughter isotopes).
Measurement of parent to daughter isotope ratio x length of half-life = age of material.

Decay Parameters

The following table illustrates decay parameters for radioactive decay pairs:

Percent of Parent Atoms (P)	Percent of Daughter Atoms (D)	Half-lives Elapsed	Age
$100.0$	$0.0$	$0$	$0.000 \times T_{1/2}$
$98.9$	$1.1$	$1/64$	$0.015 \times T_{1/2}$
$97.9$	$2.1$	$1/32$	$0.031 \times T_{1/2}$
$95.8$	$4.2$	$1/16$	$0.062 \times T_{1/2}$
$91.7$	$8.3$	$1/8$	$0.125 \times T_{1/2}$
$84.1$	$15.9$	$1/4$	$0.250 \times T_{1/2}$
$70.7$	$29.3$	$1/2$	$0.500 \times T_{1/2}$
$50.0$	$50.0$	$1$	$1.000 \times T_{1/2}$
$35.4$	$64.6$	$1 \frac{1}{2}$	$1.500 \times T_{1/2}$
$25.0$	$75.0$	$2$	$2.000 \times T_{1/2}$
$12.5$	$87.5$	$3$	$3.000 \times T_{1/2}$
$6.2$	$93.8$	$4$	$4.000 \times T_{1/2}$
$3.1$	$96.9$	$5$	$5.000 \times T_{1/2}$

Radiometric Dating - Isotope Systems

Many different isotope systems are used for radiometric dating.
Examples include: U-Pb, K-Ar, Rb-Sr, C-N, Th-Pb, and more.

Parent - Daughter Isotopes and Half-Lives

Parent Isotope	Daughter Isotope	Half-Life
Uranium 238	Lead 206	4.5 billion years
Uranium 235	Lead 207	704 million years
Thorium 232	Lead 208	14 billion years
Rubidium 87	Strontium 87	48 billion years
Potassium 40	Argon 40	1.3 billion years
Carbon 14	Nitrogen 14	5730 years

Uranium-238 Decay Products

The decay of Uranium-238 into Lead-206 involves a series of intermediate decay products:

Some Decay Products of Uranium-238	Decay Particle Produced	Half-Life
Uranium-238	alpha	4.5 billion years
Radium-226	alpha	1600 years
Radon-222	alpha	3.82 days
Polonium-218	alpha	3.1 minutes
Lead-214	beta	26.8 minutes
Bismuth-214	beta	19.7 minutes
Polonium-214	alpha	$1.6 \times 10^{-4}$ second
Lead-210	beta	20.4 years
Bismuth-210	beta	5.0 days
Polonium-210	alpha	138 days
Lead-206	none	stable

U-Pb dating is used for old geological materials because of this decay chain.