What is Radiometric Dating?
Radiometric dating is a geochronological technique used to determine the absolute age of rocks, minerals, and organic materials by measuring the ratio between a parent isotope (radioactive) and its daughter isotope (decay product). Unlike relative dating (stratigraphy, biostratigraphy), which only establishes chronological order, radiometric dating assigns numerical ages in years with quantifiable uncertainties.
The method was proposed by Ernest Rutherford in 1905 and systematized by Bertram Boltwood in 1907, who performed the first U-Pb mineral datings, obtaining ages of up to 2,200 Ma — a result that dramatically extended the geological timescale accepted at the time.
Radioactive Decay Law
Every radioactive isotope decays at a constant rate, independent of external conditions (pressure, temperature, chemical state). This behavior was described by Rutherford and Soddy (1902) as a statistical law: each nucleus has a fixed probability λ of decaying per unit time, resulting in an exponential decrease of the population.
Exponential decay law
N(t)=N0⋅e−λt Where N₀ is the initial number of parent atoms, N(t) is the amount remaining after time t, and λ is the decay constant (probability of disintegration per unit time).
Important Note: The decay constant λ is an intrinsic property of the atomic nucleus, governed by the weak nuclear interaction (β decay) or the Coulomb barrier (α decay). It is immutable under changes in temperature, pressure, or chemical composition — a fundamental condition for the validity of every radiometric clock.
Half-Life (t½) and Decay Constant
The half-life is the time required for half of the radioactive atoms in a sample to decay. It is obtained by setting N(t½) = N₀/2 in the exponential law and solving:
Decay constant
λ=t1/2ln2 Half-life
t1/2=λln2 After 1 half-life, 50% of the parent remains; after 2, 25%; after 3, 12.5%, and so on. Beyond ~10 half-lives, less than 0.1% remains, making measurement impractical due to statistical noise.
Method A — Remaining Fraction
When the percentage of the original parent isotope remaining in the sample is known (typical in Carbon-14 dating, where the current activity is compared to the atmospheric one), the age is calculated by solving for t from the exponential law:
Age from remaining fraction
t=−λ1ln(100P%) In practice, ¹⁴C is measured by Accelerator Mass Spectrometry (AMS) or liquid scintillation counting. Calibration with dendrochronology (IntCal20 curve) corrects for historical variations in atmospheric ¹⁴C concentration.
Method B — Daughter/Parent Ratio (D/P)
In rock geochronology, the ratio between atoms of the daughter isotope (D) and parent isotope (P) currently present is measured. Since D = N₀ − N(t) and P = N(t), the geochronological age equation becomes:
Age from D/P ratio
t=ln2t1/2ln(1+PD) This method is ideal for systems like U-238/Pb-206, K-40/Ar-40, and Rb-87/Sr-87, where the daughter isotope accumulates in the rock and can be measured with precision by Thermal Ionization Mass Spectrometry (TIMS) or ICP-MS.