Absolute Dating: Radioactive Decay & Half-Life

Relative dating tells you which page came first. Radiometric dating tells you the exact year it was printed — within well-understood uncertainty.

Intro GeologyUni Year 1
⏱️ About 20 min
Absolute Dating: Radioactive Decay & Half-Life — illustration
Illustrative image (AI-generated).

A zircon crystal no larger than a grain of sand can whisper its birth date across four billion years. It does so not by memory, but by chemistry: the uranium trapped inside it slowly transforms into lead at a rate so constant that geologists use it as a stopwatch. Welcome to radiometric dating — the tool that turned Earth's history from a relative stack of layers into a calendar with real numbers.

💡
The big idea: Unstable parent isotopes decay into stable daughter products at a rate characterized by a constant half-life. By measuring the ratio of parent to daughter atoms in a mineral and knowing the half-life, geologists can calculate an absolute age. But the calculation rests on a critical assumption: the mineral has been a closed system since it formed, neither gaining nor losing parent or daughter atoms. Ages are reported with uncertainty, not as single exact numbers.
🎯 By the end, you'll be able to
  • Explain radioactive decay as a probabilistic process with a constant half-life
  • Calculate an age from a parent/daughter ratio and a half-life
  • State the closed-system assumption and explain why a mineral must not have lost or gained parent or daughter atoms
  • Recognize that radiometric ages carry analytical uncertainty and are reported with error bars
📎 Helpful to know first

From relative to absolute time

Relative dating orders events beautifully, but it cannot tell you how long ago something happened. For that, geologists need a natural clock — a process that proceeds at a known, constant rate and leaves a readable record in rock.

Radioactive decay is that clock. Certain isotopes are unstable: their nuclei spontaneously break down, emitting particles and energy, and transform into a different element (the daughter product). This decay is random for any single atom, but for a large collection of atoms it is astonishingly predictable. The time it takes for half of the parent atoms to decay is called the half-life, and it is a constant for each isotope.

🔑 Half-life is constant and independent of environment
The half-life of a given isotope does not change with temperature, pressure, chemical environment, or magnetic fields. A uranium-238 atom in a volcano decays at the same rate as one in a glacier. That insensitivity is what makes radiometric dating reliable across Earth's entire history.
\[ N = N_0 \left(\frac{1}{2}\right)^{t / t_{1/2}} \]
The number of parent atoms N remaining after time t, starting from N₀, with half-life t½. Equivalently, the fraction remaining is (1/2)^(t/t½).

The closed-system assumption

The radiometric age equation is simple, but it relies on one enormous assumption: the mineral has behaved as a closed system since it crystallized. That means no parent atoms escaped, no daughter atoms leaked out, and no extra daughter atoms leaked in.

In reality, systems are not perfectly closed. A crystal may crack, allowing water to carry lead away. A heating event may reset the clock by driving out daughter argon gas. Geologists deal with this by choosing minerals and methods that are robust in the expected conditions: zircon for uranium-lead (it strongly rejects lead during growth and resists resetting), biotite for potassium-argon (it traps argon well until heated).

⚠️ Misconception: 'Radiometric dating gives one exact age'
A reported age such as 2.50 ± 0.05 Ga is not a single exact number. The ± 0.05 Ga captures analytical uncertainty in the mass-spectrometer measurement, uncertainty in the half-life value, and uncertainty about whether the system was truly closed. The age is a best estimate with a confidence interval, not a precise point.
⚠️ Misconception: 'Half-life means the sample is gone after one half-life'
After one half-life, half the parent remains. After two half-lives, one-quarter remains. After ten, about 0.1% remains. The parent never truly reaches zero — it approaches zero asymptotically. This is why very ancient rocks are dated with long-half-life isotopes like U-Pb, and young rocks are dated with short-half-life isotopes like C-14.

How the age is calculated from a ratio

In practice, geologists measure the ratio of parent to daughter atoms. If the daughter started at essentially zero — which is true for many systems, such as Ar-40 in biotite or Pb-206 in zircon — then the parent fraction tells you directly how many half-lives have elapsed.

For example, if a mineral has equal amounts of parent and daughter, the parent fraction is 1/2, so exactly one half-life has passed. If the parent fraction is 1/4, two half-lives have passed. The general formula for age, when daughter started at zero, is:

\[ t = \frac{t_{1/2}}{\ln 2} \cdot \ln\!\left(1 + \frac{D}{P}\right) \]
Age t from the daughter/parent ratio D/P, where t½ is the half-life. This form is convenient because mass spectrometers measure D/P directly.
📝 Worked example: A biotite sample has a ⁴⁰K/⁴⁰Ar ratio of 1:7. The half-life of ⁴⁰K is 1.25 Ga. Assuming no initial argon, what is the age of the biotite?
  1. The parent fraction = parent / (parent + daughter) = 1 / (1 + 7) = 1/8.
  2. 1/8 = (1/2)³, so three half-lives have elapsed.
  3. Age = 3 × 1.25 Ga = 3.75 Ga.
  4. (Using the logarithmic formula: t = (1.25 / 0.693) × ln(1 + 7) = 1.803 × 2.079 = 3.75 Ga.)
✓ 3.75 Ga (3.75 billion years).
🎮 Decay-Curve Plotter LIVE

Interactive D3 plot showing parent and daughter abundances versus time for a selectable isotope, with draggable ratio readout and calculated age.

Pick an isotope, watch the parent and daughter curves evolve, and solve numeric age problems interactively.
✏️ Practice: A biotite grain contains ⁴⁰K/⁴⁰Ar = 1:3 (same isotope system, t½ = 1.25 Ga). What is its age in Ga?
Ga
Solution
  1. Parent fraction = 1 / (1 + 3) = 1/4.
  2. 1/4 = (1/2)², so two half-lives have elapsed.
  3. Age = 2 × 1.25 Ga = 2.50 Ga.
✏️ Practice: A granite has a U-Pb age of 2.50 ± 0.05 Ga. If the true age were exactly 2.52 Ga, would the measurement be consistent with the reported uncertainty?
Solution
  1. The reported range is 2.50 − 0.05 = 2.45 Ga to 2.50 + 0.05 = 2.55 Ga.
  2. 2.52 Ga falls inside this interval.
  3. Therefore the answer is yes (enter 1 for yes, 0 for no).

Check your understanding

1. What does the closed-system assumption require?
A closed system means no parent or daughter atoms have entered or left the mineral since it formed. If the system is open, the calculated age will be wrong.
2. A mineral has equal amounts of parent and daughter. How many half-lives have passed?
Equal parent and daughter means the parent fraction is 1/2, which corresponds to exactly one half-life.
3. Why is a radiometric age reported as 2.50 ± 0.05 Ga rather than a single number?
Radiometric ages carry uncertainty from measurement precision, decay-constant precision, and assumptions about the system's history. The ± range expresses that uncertainty honestly.
🔎 Related lessons
Relative Dating Principles The Geologic Time Scale Fossils & Faunal Succession
✅ Key takeaways
  • Radioactive decay proceeds at a constant half-life, providing a natural clock for dating rocks.
  • Age is calculated from the parent/daughter ratio, assuming the system has been closed since crystallization.
  • Radiometric ages are reported with uncertainty (±), not as single exact numbers.
  • After one half-life, half the parent remains; the parent never truly reaches zero.
➡️ With absolute ages in hand, geologists can now build the master calendar of Earth history — the geologic time scale.
Want to test yourself on this? Try the Science practice tests →
🎓 Go deeper: university courses & trusted references

Handpicked external material for this module — for when you want the full university treatment of geologic time & stratigraphy.

External sites are listed for reference only. This course is independent and has no affiliation with, or endorsement from, the institutions named.