Comprehensive Study Notes on Isotopes and Radiometric Dating

Tutor Center Information

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    • Hours:
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Carbon Isotopes

  • Observed carbon isotopes: 8C – 22C
  • Natural abundance of carbon isotopes:
    • ^{12}C: < 99% of natural carbon atoms
    • ^{13}C: ~ 1% of natural carbon atoms
    • ^{14}C: ~ 0.01% of natural carbon atoms

Isotopes and Radioactive Decay

  • Isotopes: Atoms of the same element with different numbers of neutrons.
  • Radioactive isotopes: Spontaneously decay, emitting rays and subatomic particles.
  • Radioactive decay: Measured in “Half-lives”.

Half-Life Illustration

  • Coin flip analogy: Demonstrates how half-life works.
  • If the half-life is one day:
    • < 1,000 remaining at 10 days
    • < 100 remaining at 14 days
  • Unpredictability of individual events, but predictable group behavior.

Carbon-14 Dating

  • Half-life: Measurement of radioactive decay.
  • Half-life of ^{14}C: 5730 years (+/- 40 years).
  • Dating method: Determine the age of a sample by measuring the change in the ratio of ^{14}C to ^{12}C relative to the known normal ratio in living organisms.
  • Nobel Prize: The carbon-14 dating method was recognized with the Nobel Prize in 1960.

Carbon-14 Dating Applications

  • Age range: Can date materials younger than approximately 50,000 years before present.
  • Examples: Dead Sea Scrolls, parchment, papyrus.
  • Discovery: The Dead Sea Scrolls were discovered between 1946 and 1956 in the “West Bank”.
  • Age: Approximately 1700-2400 years old.

Carbon-14 Decay Chart

  • Illustrates the exponential decay of Carbon-14 over time.
  • After 5730 years (one half-life), 50% of the initial ^{14}C remains.
  • After 11460 years (two half-lives), 25% of the initial ^{14}C remains.

Carbon-14 Cycle

  • ^{14}C formation: Formed in the atmosphere.
  • ^{14}CO_2: Plants take in carbon dioxide during photosynthesis.
  • Food chain: Enters the food chain through autotrophs (producers) and heterotrophs (herbivores and omnivores).

Carbon-14 Material Dating

  • Age range: Can date materials younger than ~50,000 years before present.
  • Examples: Bone, wood, shells, pollen, coprolites, pottery.

Carbon-14 Coprolite Analysis

  • Fossil poop (coprolites): Reveals the role of giant birds in New Zealand’s ecosystem.
  • DNA analysis: Identifies what animal pooped and what it had eaten.
  • ^{14}C dating: Determines when it pooped.
  • Oldest Coprolites: About ~1557 years old

The Iceman (Ötzi)

  • Discovery: Found frozen in the Alps in 1991.
  • Initial misjudgment: Initially thought to be a recent finding but soon realized to be old.
  • Studies: Extensive research on his clothes, weapons, tools, tattoos, health, wounds, parasites, diet, genes.
  • Question: When did he live and die?

Ötzi's Age

  • Dating: Approximately 3300 BC.
  • Method: Based on ^{14}C dating.

Woolly Mammoth Dating Problem

  • Discovery: A baby woolly mammoth carcass found in Siberia in 1977 (named Dima).
  • ^{14}C content: ^{1/128} the “normal” amount of ^{14}C.
  • Half-life of ^{14}C: 5730 years.
  • Problem: How long ago did this baby die?

Woolly Mammoth Solution

  • Seven half-lives: Needed to reach ^{1/128} of the original amount (2^7 = 128).
  • Calculation: 7
    eq 5730 = 40,110 years old.

Half-Lives of Other Isotopes

  • Phosphorus-32:
    • Half-life: 14.3 days
    • Uses: DNA sequencing
  • Sulfur-35:
    • Half-life: 87.9 days
    • Uses: Labeling proteins
  • Cobalt-60:
    • Half-life: 5.3 years
    • Uses: Cancer therapy
  • Hydrogen-3:
    • Half-life: 12.4 years
    • Uses: Metabolic studies
  • Uranium-235:
    • Half-life: 704 million years
  • Potassium-40:
    • Half-life: 1.3 billion years
  • Uranium-238:
    • Half-life: 4.5 billion years
  • Thorium-232:
    • Half-life: 14 billion years
  • Rubidium-87:
    • Half-life: 49 billion years
  • Ernest Rutherford: Father of nuclear physics, half-life, model of atom, subatomic particles, Radiometric dating, Nobel Prize 1908

Age of the Earth

  • Estimated age: ~4.6 Billion years.
  • Evidence: Oldest rocks on Earth (so far).
  • Acasta Gneisses: Found near Great Slave Lake, Canada, 4.03 Billion years old.

Evidence for Earth's Age: Zircon

  • Oldest minerals: Contain zircon (zirconium silicate).
  • Worldwide distribution: Found worldwide, including Llano County (~1.3 billion years before present).

Zircon Dating

  • Composition: Zircons contain uranium and thorium.
  • Dating method: Radiometric dating based on the decay of radioactive isotopes of uranium and thorium.

Oldest Zircon

  • Location: Jack Hills of Western Australia.
  • Age: Dated as 4,404 +/- 8 Myr (million years).

Oldest Materials on Earth

  • Ca-Al-rich inclusions: Found in some meteorites.
  • Meteor Crater, Arizona: Formed about 50,000 years ago.
  • Age: About 4.5 billion years old.
  • Canyon Diablo Meteor: ~3,900 feet ~3/4 mile

Allende Meteorite

  • Event: Fireball near Allende, Chihuahua, Mexico on February 8, 1969, at 1:05 a.m.
  • Size: Meteorite estimated to be > 2 tons broke up in the atmosphere.
  • Inclusions: Dated to 4.567 billion years old (+/- 1%).

Summary of Earth's Age Evidence

  • Oldest rocks: 4.03 billion years old.
  • Oldest minerals: 4.4+ billion years old.
  • Meteorites: 4.5+ billion years old.
  • Oldest dated moon rocks: 4.4 - 4.5 billion years old.

Isotopes and Radiation Summary

  • Isotopes: Variations of atoms that differ in the number of neutrons.
  • Radiation source: Radioactive isotopes are a source of radiation.
  • Radiation effects: Radiation can be harmful and/or useful.
  • Carbon-14: Useful for dating recent events.
  • Other elements: Used for dating older events.

Carbon-14 Dating Summary

  • Half-life of ^{14}C: 5730 years (+/- 40 years).
  • Applicability: Can potentially date anything that was once alive.
  • Age range: Back to about 50,000 years before present.
  • Vindija Cave, Croatia: Both Neandertal and modern human remains were found, Neandertal remains date to ~40,000 and oldest “modern” remains to ~8,000 years before present.

Carbon-14 Dating Limitations

  • Limitations: Known and continue to be studied.
  • Aquatic organisms: Dating can be affected in some aquatic organisms and animals that feed on them.
  • Nuclear explosions: Nuclear explosions have altered ^{14}C ratios.

Meteorite Older Than Earth

  • Discovery: Jan. 7, 2016, a rock “older than Earth” was found in the Australian Outback.
  • Fall date: Fell on November 27, 2015.
  • Age: Dated to 4.5 billion years.

Molecules and Compounds

  • Molecule: A group of atoms of the same element bonded together.
  • Compound: A group of atoms of different elements bonded together.

Water Molecules

  • Covalent bonds
    • water molecules are held together by strong covalent bonds
  • Polar molecule
    • water is a polar molecule
  • Hydrogen bond
    • Individual molecules hydrogen bond (weak) to other water molecules

Properties of Water

  • Liquid at room temperature
  • Solvent for polar molecules
  • Cohesive
  • Temperature rises and falls slowly
  • High heat of vaporization
  • Frozen water is less dense than liquid water

Saline Solution

  • 0. 9% Sodium Chloride Injection USP
  • Sterile Preserved
  • For use in Heat (Thermal) Disinfection
  • For Rinsing and Storage of Soft (Hydrophilic) Contact Lenses

Humidity Levels

  • Average above 70% humidity
  • Average below 40% humidity

Water Dissociation

  • H-O-H
    ightharpoonup H^+ + OH^-
  • water
    ightharpoonup hydrogen ion + hydroxide ion

Acidity

  • In an aqueous solution:
    • If H^+ concentration > OH^-, the solution is acidic.
    • If OH^- concentration > H^+, the solution is basic.

pH Scale

  • Measures acidity or alkalinity of a solution.
  • Neutral = 7
  • Why 7? In pure water, 1 molecule out of 10^7 dissociates (1/10,000,000).