How do we measure the absolute age of a rock using radioactive decay?
Radiometric dating: radioactive decay of unstable parent isotopes to stable daughter isotopes; the concept of half-life as a constant; the use of parent-to-daughter ratios to calculate absolute ages; the main isotopic systems (uranium-lead, potassium-argon and carbon-14) and their suitable age ranges; the assumptions and limitations of radiometric dating; the combination of absolute and relative dating.
A focused answer to the OCR H414 dot point on radiometric dating. Covers radioactive decay of parent to daughter isotopes, half-life as a constant, calculating absolute ages from parent-to-daughter ratios, the uranium-lead, potassium-argon and carbon-14 systems and their ranges, the assumptions and limitations, and combining absolute with relative dating.
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What this dot point is asking
OCR wants you to explain radioactive decay of parent to daughter isotopes, define half-life as a constant, calculate absolute ages from parent-to-daughter ratios, name the main isotopic systems (uranium-lead, potassium-argon, carbon-14) and their suitable ranges, state the assumptions and limitations, and combine absolute with relative dating.
The answer
Radioactive decay and half-life
Some isotopes are unstable (radioactive) and decay spontaneously and randomly into a stable daughter isotope, releasing radiation. The rate is constant for a given isotope and is described by the half-life.
Because the half-life is constant, the proportion of parent left falls predictably: after half-life remains, after half-lives , after half-lives , and so on. This is captured by:
where is the original number of parent atoms, the number remaining, and the number of half-lives elapsed.
Calculating an age from the parent-to-daughter ratio
When a mineral crystallises it traps parent atoms but (ideally) no daughter. Over time, parent decays to daughter, so the parent-to-daughter ratio records the age. The method:
- Find the fraction of parent remaining from the ratio.
- Work out how many half-lives that fraction corresponds to.
- Multiply the number of half-lives by the half-life to get the age.
The main isotopic systems
The half-life must suit the age being measured:
- Uranium-lead (U-Pb). Very long half-lives (hundreds of millions to billions of years); used to date the oldest rocks and the age of the Earth.
- Potassium-argon (K-Ar). Intermediate half-life; widely used to date igneous rocks (for example lavas and ash bands).
- Carbon-14 (C-14). Short half-life (about years); used only for recent organic material (up to roughly to years).
Assumptions and limitations
Radiometric ages are only valid if certain assumptions hold:
- The system has remained closed (no parent or daughter added or lost since formation).
- The initial amount of daughter is known (ideally zero, or correctable).
- A suitable material and isotope are used for the age range.
If the rock has been heated, weathered or altered, daughter (for example argon gas) can escape, giving a wrong age.
Combining absolute and relative dating
Radiometric dating gives absolute ages (in years) but only for suitable minerals (mostly igneous). Relative dating orders all the rocks (including sediments). Combining them, an absolute date from a lava or ash band can be tied into a relative sequence, calibrating the geological time scale in years.
Examples in context
Example 1. Dating the Earth with uranium-lead. The very long half-lives of the uranium-lead system allow it to date the oldest meteorites and minerals, giving the age of the Earth at about billion years.
Example 2. Calibrating an ash band. Potassium-argon dating of a volcanic ash band within a sedimentary sequence ties an absolute age into the relative succession, anchoring the surrounding biozones in years.
Try this
Q1. Define the half-life of a radioactive isotope. [1 mark]
- Cue. The time taken for half of the parent atoms in a sample to decay to the daughter isotope.
Q2. A mineral has a parent-to-daughter ratio of . State how many half-lives have elapsed. [1 mark]
- Cue. One half-life (half the parent remains, half has become daughter).
Q3. Explain why uranium-lead, not carbon-14, is used to date a billion year old rock. [2 marks]
- Cue. Carbon-14 has a short half-life and is useful only up to about years; uranium-lead has very long half-lives suited to dating ancient rocks billions of years old.
Exam-style practice questions
Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
OCR H414/01 20204 marksA mineral contains a parent isotope and its stable daughter in the ratio 1 part parent to 3 parts daughter. The half-life of the parent is 700 million years. Calculate the age of the mineral, showing your working.Show worked answer →
Convert the ratio to a fraction remaining, count half-lives, then multiply.
Fraction of parent remaining. The ratio is parent to daughter, so out of every original parent atoms, remains and have decayed. The fraction of parent remaining is .
Number of half-lives. After each half-life the parent halves: after half-life remains, after half-lives remains. So corresponds to half-lives.
Age.
The mineral is billion years old. Markers reward converting the ratio to remaining, recognising this as half-lives, and multiplying by the half-life.
OCR H414/01 20184 marksExplain why carbon-14 dating cannot be used to date a granite that is 400 million years old, and name a more suitable isotopic system.Show worked answer →
Tie the half-life to the age range, then name an alternative.
Carbon-14 has a short half-life (about ). After about half-lives (roughly to ) so little carbon-14 remains that it cannot be measured accurately. A granite years old is far beyond this range, so essentially all the carbon-14 would have decayed and no measurable age could be obtained.
Carbon-14 also needs organic carbon, which a granite does not contain.
A more suitable system. Uranium-lead (or potassium-argon) dating, which uses isotopes with very long half-lives (hundreds of millions to billions of years), is suitable for dating ancient igneous rocks such as granite.
Markers reward the short half-life and limited range of carbon-14 (and its need for organic material) and naming a long-half-life system (uranium-lead or potassium-argon).
Related dot points
- Relative dating: the principles used to order geological events (superposition, original horizontality, cross-cutting relationships, included fragments and faunal succession); the recognition of way-up evidence; the application of these principles to construct the geological history of a cross-section, including faults, intrusions and unconformities.
A focused answer to the OCR H414 dot point on relative dating. Covers superposition, original horizontality, cross-cutting relationships, included fragments and faunal succession, way-up evidence, and how to apply these principles to reconstruct the geological history of a cross-section with faults, intrusions and unconformities.
- The geological record: the hierarchy of the geological time scale (eon, era, period, epoch) and the major divisions (Precambrian and the Phanerozoic eras); correlation of strata by lithostratigraphy (matching rock units) and biostratigraphy (matching fossils and biozones); the use of marker horizons such as volcanic ash bands; the distinction between rock units (systems) and time units (periods).
A focused answer to the OCR H414 dot point on the geological time scale and correlation. Covers the eon, era, period and epoch hierarchy and the major divisions, correlation by lithostratigraphy and biostratigraphy, the use of marker horizons such as ash bands, and the distinction between rock units and time units.
- Fossils: the conditions that favour preservation (rapid burial, anoxia, hard parts, fine sediment); the modes of preservation (moulds and casts, permineralisation, carbonisation, and preservation in amber or ice); the properties of a good index (zone) fossil (abundant, widespread, easily recognised, short stratigraphic range); the distinction between body and trace fossils.
A focused answer to the OCR H414 dot point on fossils. Covers the conditions favouring preservation, the modes of preservation (moulds and casts, permineralisation, carbonisation, amber and ice), the properties of a good index or zone fossil, and the distinction between body and trace fossils.
- Evolution and the fossil record: evidence for evolution from the fossil record (morphological change through time, transitional forms, adaptive radiation); the models of evolutionary change (gradualism versus punctuated equilibrium); mass extinctions and their causes and effects (for example the end-Permian and end-Cretaceous events); the incompleteness and biases of the fossil record.
A focused answer to the OCR H414 dot point on evolution. Covers the fossil evidence for evolution (morphological change, transitional forms, adaptive radiation), the gradualism and punctuated equilibrium models, mass extinctions (the end-Permian and end-Cretaceous events) and their causes and effects, and the incompleteness and biases of the fossil record.
- Earth structure: the layered internal structure of the Earth (crust, mantle, outer core and inner core) and the contrasts between oceanic and continental crust; the seismic evidence for the layering (changes in wave velocity at boundaries such as the Moho); the P and S wave shadow zones as evidence for a liquid outer core; the link between the core and the Earth's magnetic field.
A focused answer to the OCR H414 dot point on Earth structure. Covers the crust, mantle, outer core and inner core, oceanic versus continental crust, the seismic evidence for the layering (velocity changes and the Moho), the P and S wave shadow zones as evidence for a liquid outer core, and the link between the core and the magnetic field.
Sources & how we know this
- OCR A Level Geology (H414) Specification — OCR (2017)