Key Formulas & Equations
Decay Constant: λ = ln(2)/t½
Age Calculation: t = (1/λ) × ln(N₀/N)
Half-Life: t½ = 0.693/λ
C-14 Half-Life: 5,730 years
Effective Range: Up to ~50,000 years
Calibration: Required due to atmospheric C-14 variation
Phanerozoic Eon: 541 Ma - present (visible life)
Precambrian: 4.6 Ga - 541 Ma (88% of Earth's history)
Stratigraphic Principles: Original horizontality, superposition, cross-cutting
Taphonomy: Study of decay and fossilization processes
Index Fossils: Widespread, short-lived species for dating
Biostratigraphy: Correlation using fossil assemblages
Punctuated Equilibrium: Rapid change + stasis
Phyletic Gradualism: Slow, continuous change
Mass Extinction: Loss of >75% species in short time
Core Concepts
Fossil Formation
Processes that preserve remains: permineralization, replacement, casts/molds, and exceptional preservation (amber, tar pits, frozen).
Geologic Time
The 4.6 billion year history of Earth divided into eons, eras, periods, and epochs. Based on stratigraphy and radiometric dating.
Evolution
The change in heritable characteristics of populations over generations. Mechanisms: natural selection, genetic drift, mutation, gene flow.
Dinosaur Paleontology
Study of dinosaurs (Triassic to Cretaceous, 230-66 Ma). Includes taxonomy, behavior, physiology, and extinction theories.
Mass Extinctions
Five major mass extinctions in Earth's history. End-Permian (252 Ma): 96% species lost. End-Cretaceous (66 Ma): 75% species lost (dinosaurs).
Paleoecology
Study of ancient environments and ecosystems. Uses fossils to reconstruct past climates, habitats, and food webs.
Vertebrate Evolution
Evolution of vertebrates: fish → amphibians → reptiles → mammals and birds. Key transitions: jaws, limbs, feathers, endothermy.
Human Evolution
Evolution of hominins from apes. Key species: Ardipithecus, Australopithecus, Homo erectus, Homo sapiens. Bipedalism, tool use, brain expansion.
Worked Examples
Example 1: Carbon-14 Dating
Problem: A fossil has 25% of original C-14. Calculate its age (t½ = 5,730 years).
Solution:
N/N₀ = 0.25 = (1/2)n → n = 2 half-lives
Age = 2 × 5,730 = 11,460 years
Example 2: Decay Constant
Problem: Calculate decay constant for C-14 (t½ = 5,730 years).
Solution:
λ = ln(2)/t½ = 0.693/5,730 = 1.21×10⁻⁴ year⁻¹
Example 3: Radioactive Decay
Problem: If 10g of a substance decays to 2.5g in 2 half-lives, verify the relationship.
Solution:
N = N₀(1/2)n = 10 × (1/2)² = 10 × 0.25 = 2.5 g ✓
Practice Problems
Problem 1
Calculate age of fossil with 12.5% C-14 remaining.
Answer: 3 half-lives = 17,190 years
Problem 2
Identify the duration of the Phanerozoic Eon.
Answer: 541 million years to present
Problem 3
Calculate decay constant for a substance with t½ = 1,000 years.
Answer: λ = 0.693/1,000 = 6.93×10⁻⁴ year⁻¹
Problem 4
Identify the percentage of species lost in the End-Permian extinction.
Answer: 96%
Problem 5
Calculate remaining amount after 3 half-lives if initial = 100g.
Answer: N = 100 × (1/2)³ = 12.5 g
Problem 6
Identify the principle stating that older layers are below younger layers.
Answer: Law of Superposition
Problem 7
Calculate age if N/N₀ = 0.5 and λ = 10⁻⁴ year⁻¹.
Answer: t = ln(2)/10⁻⁴ = 6,930 years