How do we put a number of years on a rock or fossil?
Explain radioactive decay and half-life and use the Reference Tables Radioactive Decay Data to calculate the absolute age of a sample from the ratio of remaining radioactive isotope to its decay product.
A Regents answer on radioactive dating: what radioactive decay and half-life mean, the Reference Tables Radioactive Decay Data (Carbon-14 half-life 5700 years, Uranium-238 4.5 billion years), how to count half-lives from the ratio of parent to daughter, why Carbon-14 dates recent material and Uranium-238 dates ancient rock, with worked half-life calculations.
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What this topic is asking
The Regents wants you to explain radioactive decay and half-life and to use the Reference Tables Radioactive Decay Data to find the absolute (numerical) age of a sample by counting half-lives from the ratio of remaining radioactive isotope to its decay product. This is the one calculation that gives ages in years.
Radioactive decay and half-life
Because the half-life is constant, the ratio of parent to daughter is a clock. As time passes, the parent decreases and the daughter increases in a fixed pattern:
| Half-lives passed | Parent remaining | Daughter formed |
|---|---|---|
| 0 | 100% (all) | 0% |
| 1 | 50% (half) | 50% |
| 2 | 25% (one-quarter) | 75% |
| 3 | 12.5% (one-eighth) | 87.5% |
Calculating absolute age
The Reference Tables Radioactive Decay Data give the half-life of each isotope. To find an age:
- From the ratio of remaining parent (or parent to daughter), count the number of half-lives.
- Multiply by the half-life:
Try this
Q1. Define half-life. [1 point]
- Cue. The time for half of the radioactive atoms in a sample to decay into the decay product.
Q2. A rock has equal amounts of Uranium-238 and lead-206. Using the Reference Tables (half-life 4.5 billion years), find its age. [2 points]
- Cue. A 50:50 ratio means one half-life has passed, so the age is 1 x 4.5 billion = 4.5 billion years.
Exam-style practice questions
Practice questions written in the style of NYSED exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Regents (style)2 marksPart B-2. A sample of organic material contains one-quarter of its original Carbon-14. Using the Reference Tables (Carbon-14 half-life = 5700 years), calculate the age of the sample. Show your reasoning.Show worked answer →
A 2-point calculation using the Radioactive Decay Data.
1 point for the number of half-lives, 1 point for the age.
One-quarter remaining means two half-lives have passed (after one half-life half remains, after two half-lives one-quarter remains).
Age = number of half-lives x half-life = 2 x 5700 years = 11,400 years.
Markers reward identifying two half-lives from the one-quarter ratio and multiplying by 5700 years. A common error is using one half-life for one-quarter; one-quarter is two half-lives.
Regents (style)3 marksPart C. (a) Define half-life. (b) A rock contains equal amounts of Uranium-238 and its decay product (lead-206). Using the Reference Tables (Uranium-238 half-life = 4.5 billion years), determine the age of the rock. (c) Explain why Carbon-14 cannot be used to date a rock billions of years old.Show worked answer →
A 3-point extended-response question.
(a) 1 point: half-life is the time it takes for half of the radioactive atoms in a sample to decay into the decay product.
(b) 1 point: equal amounts of Uranium-238 and lead-206 means half has decayed, so one half-life has passed: age = 1 x 4.5 billion years = 4.5 billion years.
(c) 1 point: Carbon-14 has a short half-life (5700 years), so after only tens of thousands of years almost all of it has decayed and too little remains to measure; it cannot reach billions of years.
Markers reward the half-life definition, recognizing a 50:50 ratio as one half-life (4.5 billion years), and the short-half-life reasoning for Carbon-14's limit.
Related dot points
- Apply the principles of relative dating (superposition, original horizontality, cross-cutting relationships, inclusions and unconformities) to order events in a sequence of rock layers.
A Regents answer on relative dating: the law of superposition, original horizontality, cross-cutting relationships, inclusions, and how unconformities record missing time, used to put events in order in a cross-section, plus how faults, intrusions and contact metamorphism fit the sequence, with worked exam questions.
- Explain how fossils form, what index fossils are, and how fossils are used to correlate rock layers between distant locations and to infer past environments, using the Reference Tables.
A Regents answer on fossils and correlation: how fossils form, the features of a good index fossil (widespread, short-lived, easily recognized), how index fossils and matching rock match (correlate) layers between distant outcrops, what fossils reveal about past environments and evolution, and how to read the Geologic History of New York State chart, with worked exam questions.
- Describe how the geologic time scale is divided (eons, eras, periods, epochs), how its boundaries mark major changes in life, and use the Reference Tables geologic time scale to read ages and events.
A Regents answer on the geologic time scale: the divisions (eons, eras, periods, epochs), Precambrian time and the Paleozoic, Mesozoic and Cenozoic eras, how mass extinctions mark era boundaries, Earth's age of about 4.6 billion years, and how to read ages and events off the Reference Tables Geologic History of New York State chart, with worked exam questions.
- Use the Reference Tables Geologic History of New York State and the bedrock map to read New York's tectonic and environmental history, including ancient mountain-building, shallow seas and the most recent glaciation.
A Regents answer on New York's geologic history: how to read the Geologic History of New York State chart and the bedrock map together, the ancient mountain-building (orogenies), the shallow seas that left marine fossils and sedimentary rock, the oldest Precambrian rock of the Adirondacks, and the last ice age that shaped today's landscape, with worked exam questions.
- Use the Luminosity and Temperature of Stars diagram to classify stars, describe the Sun and nuclear fusion, and state the evidence for the Big Bang (red shift and cosmic background radiation).
A Regents answer on stars and cosmology: reading the Luminosity and Temperature of Stars (Hertzsprung-Russell) diagram, the Sun as a main sequence star powered by nuclear fusion, star color and temperature, and the red shift and cosmic background radiation as evidence for the Big Bang.
Sources & how we know this
- Reference Tables for Physical Setting/Earth Science (2011 edition) — New York State Education Department (2011)
- Regents Examination in Physical Setting/Earth Science — New York State Education Department (2026)