Se quemaron en O2 unas muestras de carbón vegetal de...

Se quemaron en $\mathrm{O}_2$ unas muestras de carbón vegetal de Stonehenge, Inglaterra, y el $\mathrm{CO}_2$ gaseoso resultante se hizo burbujear en una disolución de $\mathrm{Ca}(\mathrm{OH})_2$ (agua de cal), con la consecuente precipitación de $\mathrm{CaCO}_3$. El CaCO 3 se separó por filtración y se secó. Una muestra de $788 \mathrm{mg}$ del $\mathrm{CaCO}_3$ mostró una radiactividad de $1.5 \times 10^{-2} \mathrm{~Bq}$ debida al carbono 14. En comparación, los organismos vivos sufren 15.3 desintegraciones por minuto por gramo de carbono. Con base en la vida media del carbono 14 (5715 años), calcule la antigūedad de la muestra de carbón.

Key Concepts

Radioactivity Measurement Units

Radioactivity is often measured in becquerels (Bq), which represent one disintegration per second. Understanding and converting these units, such as converting decays per minute to becquerels, is crucial for accurately assessing the level of radioactivity in a sample and applying the appropriate decay equations in radiometric dating.

Half-life

The half-life of a radioactive isotope is the amount of time required for half of the original quantity of the isotope to decay. For carbon-14, this value is approximately 5715 years. It is a key parameter in radiometric dating techniques, as it provides a scale for determining the age of samples based on the proportion of carbon-14 that remains.

Carbon-14

Carbon-14 is a naturally occurring radioactive isotope of carbon that is formed in the upper atmosphere. It is taken up by living organisms during their lifetimes. Its decay after death, governed by its half-life, allows scientists to measure the elapsed time since the organism ceased exchanging carbon with the environment.

Exponential Decay Law

The exponential decay law describes how a quantity decreases over time at a rate proportional to its current value. In the context of radioactive decay, this law is used to model the reduction of carbon-14 in a sample, leading to the calculation of the sample's age based on the remaining amount of radioactive material.

Radiocarbon Dating

Radiocarbon dating is a method used to determine the age of organic materials by measuring the decay of carbon-14, a radioactive isotope of carbon that is incorporated into living organisms. After death, the intake of carbon stops and the carbon-14 present begins to decay at a known rate, providing a 'clock' that can be used to estimate the time since the organism died.

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