# Definition:Radiometric Dating

## Definition

**Radiometric dating** is a technique whose purpose is to work out the age $T$ of a physical object $B$.

The pieces of information are known:

- $(1): \quad$ The ratio $r_0$ of a radioactive isotope $E_R$ of a chemical element $E$ to its stable isotope $E_S$ in $B$ at the time it came into being

- $(2): \quad$ The ratio $r$ of $E_R$ to $E_S$ at the time now

- $(3): \quad$ The half-life of the radioactive isotope $E_R$

It is known from scientific investigation what $r_0$ is when a physical object is created.

It is also known from scientific investigation what the rate of radioactive decay of $E_R$ is.

Hence it can be worked out by use of the First-Order Reaction how long it would take for the ratio of $E_R$ to $E_S$ to reach its current ratio $r$.

### Radiocarbon Dating

**Radiocarbon dating** is a specific application of **radiometric dating** which is used to determine how long a piece of organic matter has been dead.

Because of bombardment by cosmic rays, the ratio of (radioactive) carbon-14 to (stable) carbon-12 in the atmosphere of Earth is fairly constant.

This ratio is known.

The ratio of carbon-14 to carbon-12 in a living organism is the same as it is in Earth's atmosphere, by biological respiration.

However, when the organism dies, it no longer respires, and the carbon in its body stays where it was at the time of its death.

As time passes, the carbon-14 decays to nitrogen-14 via the process of beta decay.

The half-life of carbon-14 is known to be $5700 \pm 40$ years.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions