How is the numerical age of a rock measured?
The principle of radiometric dating using radioactive decay and half-life, the parent-to-daughter ratio, the choice of isotope system, and the assumptions and limitations of the method.
A focused answer to WJEC and Eduqas A-Level Geology F3 on absolute dating, covering radioactive decay and half-life, calculating an age from the parent-to-daughter ratio, the choice of isotope system (uranium-lead, potassium-argon, carbon-14), and the assumptions and limitations of radiometric dating.
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What this dot point is asking
WJEC wants you to explain how radiometric dating gives a numerical (absolute) age, to use half-life and the parent-to-daughter ratio to calculate an age, to choose an appropriate isotope system for a given material, and to state the assumptions and limitations of the method. This complements relative dating: radiometric ages calibrate the relative timescale in years.
The answer
Radioactive decay and half-life
Some isotopes are radioactive: their unstable nuclei decay at a fixed, constant rate, turning a parent isotope into a stable daughter isotope. The rate is described by the half-life, the time for half of the parent atoms in a sample to decay. Because the rate is constant and unaffected by temperature, pressure or chemistry, the proportion of parent left is a reliable clock.
Measuring an age
The clock is read from the parent-to-daughter ratio. At crystallisation a mineral locks in parent atoms and (ideally) no daughter; as time passes parent decays to daughter, so the ratio falls in a predictable way. Measuring the ratio gives the number of half-lives elapsed, and multiplying by the half-life gives the age.
Choosing a system and reading a calculation
Assumptions and limitations
Radiometric dating assumes: the decay rate is constant (well established); the system has remained closed since crystallisation (no parent or daughter added or lost, for example by later heating, weathering or fluid flow); and the initial daughter content is known (often assumed zero or corrected for). It dates the time of crystallisation or closure, not deposition, so a detrital mineral can be older than the rock that contains it. Carbon-14 is limited to young, once-living material; the long-half-life systems suit old rocks but need careful sampling of fresh, unaltered minerals.
Examples in context
The age of the Earth. Uranium-lead dating of meteorites and the oldest minerals gives about 4.6 billion years for the Solar System and Earth, the headline result of radiometric dating. Dating zircons. Tiny, robust zircon crystals incorporate uranium but exclude lead at growth, making uranium-lead in zircon the gold standard for the oldest crustal ages. Calibrating the timescale. Volcanic ash layers (bentonites) interbedded with fossil-bearing sediments are dated by potassium-argon, tying numerical ages to the relative, fossil-based timescale.
Try this
Q1. Define half-life. [2 marks]
- Cue. The time taken for half the parent atoms in a sample to decay to the daughter product.
Q2. A mineral has a parent-to-daughter ratio of 1:7 for a system of half-life 50 million years. Calculate its age. [2 marks]
- Cue. 1:7 means one eighth of the parent remains, which is three half-lives, so age = 3 times 50 = 150 million years.
Q3. State two assumptions of radiometric dating. [2 marks]
- Cue. The decay rate is constant; the system has stayed closed (no parent or daughter gained or lost) since crystallisation; the initial daughter content is known.
Exam-style practice questions
Practice questions written in the style of WJEC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
WJEC Eduqas 20193 marksA mineral contains one part of a radioactive parent isotope to three parts of its stable daughter. The half-life of the parent is 700 million years. Calculate the age of the mineral.Show worked answer →
Work in fractions of the original parent, because each half-life halves the parent that remains.
The present parent-to-daughter ratio is 1:3, so the parent now is one quarter of the original (the original parent has become one part parent plus three parts daughter, a total of four).
Going from a whole to a half is one half-life, and from a half to a quarter is a second half-life, so a quarter remaining means two half-lives have passed.
Age = 2 times 700 million years = 1400 million years (1.4 billion years).
Markers reward recognising that a 1:3 ratio means a quarter of the parent remains, that this is two half-lives, and the correct arithmetic to 1.4 billion years.
WJEC Eduqas 20214 marksExplain why carbon-14 dating cannot be used to date a granite, and state a suitable isotope system that could be used instead.Show worked answer →
Carbon-14 dating measures the decay of carbon-14 in once-living material and has a half-life of only about 5730 years, so after a few tens of thousands of years almost no carbon-14 remains and the method runs out.
A granite is millions to billions of years old and contains no organic carbon, so carbon-14 is both far too short-lived and not present in the right form to date it.
A suitable system is uranium-lead (or potassium-argon or rubidium-strontium), which uses long-half-life isotopes locked into minerals such as zircon at crystallisation and so can date igneous rocks over millions to billions of years.
Markers reward the short half-life and the absence of suitable carbon, plus naming a long-half-life system such as uranium-lead for the granite.
Related dot points
- The principles of relative dating (superposition, original horizontality, cross-cutting relationships, included fragments and unconformities) and how they are combined to establish the sequence of geological events.
A focused answer to WJEC and Eduqas A-Level Geology F3 on relative dating, covering the principles of superposition, original horizontality, cross-cutting relationships, included fragments and unconformities, and how they are combined to reconstruct the order of geological events in a sequence.
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A focused answer to WJEC and Eduqas A-Level Geology F3 on fossils, covering the conditions and modes of fossil preservation, the principle of faunal succession, and how zone (index) fossils are used to correlate strata between areas and to relatively date rocks.
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- The compositional and mechanical layering of the Earth (crust, mantle, outer and inner core; lithosphere and asthenosphere) and the seismic evidence (P and S wave behaviour, shadow zones, discontinuities) used to deduce it.
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A focused answer to WJEC and Eduqas A-Level Geology F2 on internal processes, covering the sources of the Earth's internal heat (radioactive decay and residual heat), the geothermal gradient and heat flow, and how heat drives mantle convection, partial melting and metamorphism as the deep limb of the rock cycle.
Sources & how we know this
- WJEC Eduqas A-level Geology specification — WJEC Eduqas (2017)