Radiometric dating and half-life: radioactive decay and the concept of half-life; the use of parent-to-daughter ratios to calculate absolute ages; the main dating methods and their suitable age ranges (for example uranium-lead, potassium-argon, rubidium-strontium and carbon-14); the assumptions and limitations of radiometric dating; and the construction of the absolute geological time scale.

What this dot point is asking

Eduqas wants you to explain radioactive decay and half-life, to calculate absolute ages from parent-to-daughter ratios, to match the main dating methods to their age ranges (uranium-lead, potassium-argon, rubidium-strontium, carbon-14), to state the assumptions and limitations, and to describe how the absolute geological time scale is built. This is the quantitative partner to relative dating: relative dating gives the order, radiometric dating pins ages in years.

The answer

Radioactive decay and half-life

Some isotopes are unstable and decay spontaneously into a stable daughter isotope at a fixed rate, unaffected by temperature or pressure. The rate is described by the half-life.

Because the parent halves each half-life, the amount remaining follows $N = N_0 \left(\tfrac{1}{2}\right)^{n}$, where $N_0$ is the original amount and $n$ is the number of half-lives. The decay is exponential, so the parent never quite reaches zero but soon becomes unmeasurable.

Parent-to-daughter ratios

You cannot measure $N_0$ directly, but in a closed system every daughter atom came from a decayed parent, so:

The fraction of parent remaining is the parent now divided by that total, and from it you read off the number of half-lives (a half is one half-life, a quarter is two, an eighth is three). Multiplying the number of half-lives by the half-life gives the age.

The main methods and their ranges

Different isotope pairs suit different ages because of their half-lives:

• Uranium-lead (uranium-238 to lead-206, half-life about 4.5 billion years): the most precise method for very old rocks, used on zircon crystals; the basis of the oldest dates on Earth.
• Potassium-argon (potassium-40 to argon-40, half-life about 1.3 billion years): dates volcanic rocks and ash, widely used in establishing the time scale and dating early human sites.
• Rubidium-strontium (half-life about 49 billion years): for ancient igneous and metamorphic rocks.
• Carbon-14 (half-life about 5,730 years): dates recent organic material (wood, charcoal, shell, bone) up to roughly 50,000 to 60,000 years; useless for rocks because the parent decays away too quickly.

The general rule: long half-life for old rocks, short half-life for young material.

Assumptions and limitations

A radiometric age is only reliable if its assumptions hold:

• The mineral was a closed system: no parent or daughter was added or lost (later heating, metamorphism or weathering can reset or disturb the clock).
• The initial amount of daughter was zero or known.
• The decay rate has been constant (it has).
• The clock was set at a definite event (crystallisation for igneous minerals), so radiometric dates usually date igneous rocks; sedimentary rocks are dated indirectly by bracketing them between datable igneous units.

Building the absolute time scale

The geological time scale was first built by relative dating (the order of strata and their fossils), then calibrated in years by dating igneous rocks (lavas, ashes and intrusions) interbedded with or cutting the fossil-bearing strata. Combining the two gives absolute ages for the boundaries of the eras, periods and epochs.

Examples in context

Example 1. Dating the oldest rocks. Uranium-lead dating of zircon crystals gives the oldest reliable ages on Earth (over four billion years), because zircon is robust and retains uranium and lead as a closed system.

Example 2. Bracketing a fossil bed. A fossil-bearing sandstone with no datable minerals of its own can be dated by a lava flow beneath it and an ash above it: the sandstone must be younger than the flow and older than the ash.

Try this

Q1. After three half-lives, what fraction of the original parent isotope remains? [1 mark]

• Cue. One eighth ($\tfrac{1}{8}$): a half, then a quarter, then an eighth.

Q2. A mineral has a parent-to-daughter ratio of 1:1 and a half-life of 700 million years. Calculate its age. [2 marks]

• Cue. A 1:1 ratio means half the parent remains, so one half-life has passed: age $= 1 \times 700 = 700$ million years.

Q3. State one assumption that must hold for a radiometric date to be reliable. [1 mark]

• Cue. Any one of: the mineral was a closed system (no gain or loss of parent or daughter); the initial daughter was zero or known; the decay rate was constant.