Absolute dating and geologic time
Radiometric dating uses predictable changes in atoms. It works only when the sample, isotope system, and history are appropriate for the question.
Radioactive decay and Half-life
Objective: Explain radioactive decay and half-life, distinguish their meanings, and apply them to a described case.
Radioactive decay: Unstable isotopes transform at statistically predictable rates into other nuclei. Half-life: A half-life is the time required for half of a large population of parent atoms to decay. Radioactive decay is predictable for large populations of atoms, not as a schedule for one atom. After each half-life, half of the remaining parent population persists. Dating requires a suitable isotope system and interpretation of initial conditions and later changes. Numerical ages can constrain a sequence of events, but the dated event must be identified. Sedimentary deposition is not automatically dated by the crystallization age of an included mineral grain. Application: A parent isotope decreases as daughter products accumulate. This most directly illustrates radioactive decay. A closed sample retains one quarter after two half-lives. This most directly illustrates half-life.
Formulas
- Remaining parent fraction after n half-lives = (1/2)^n
Worked examples
Try itOriginal teaching scenario: A parent isotope decreases as daughter products accumulate. Which idea from this section does it most directly illustrate?Show answer
Step 1 — Read the observation: A parent isotope decreases as daughter products accumulate. Step 2 — Recall the relevant idea: Unstable isotopes transform at statistically predictable rates into other nuclei. Step 3 — Connect the observation to the idea: The scenario is an illustration of radioactive decay. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.
Try itOriginal teaching scenario: A closed sample retains one quarter after two half-lives. Which idea from this section does it most directly illustrate?Show answer
Step 1 — Read the observation: A closed sample retains one quarter after two half-lives. Step 2 — Recall the relevant idea: A half-life is the time required for half of a large population of parent atoms to decay. Step 3 — Connect the observation to the idea: The scenario is an illustration of half-life. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.
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