Le corps humain contient environ 20 % en masse de l'élément...

Le corps humain contient environ $20 \%$ en masse de l'élément carbone, et le carbone naturel contient $1,3.10^{-10} \%$ de carbone-14, qui est radioactif. Combien de désintégrations radioactives de ce carbone-14 se produit-il, en une minute, dans le corps d'un individu de $75 \mathrm{~kg}$ ?

Le corps humain contient environ $20 \%$ en masse de l'élément carbone, et le carbone naturel contient $1,3.10^{-10} \%$ de carbone-14, qui est radioactif.
Combien de désintégrations radioactives de ce carbone-14 se produit-il, en une minute, dans le corps d'un individu de $75 \mathrm{~kg}$ ?

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which unstable nuclei release energy by emitting radiation. This concept underpins the analysis of isotopic transformations over time and is essential for understanding how the number of radioactive atoms in a substance changes at an exponential rate.

Activity (Decay Rate)

Activity refers to the number of nuclear disintegrations occurring per unit time in a radioactive sample. It is determined by both the decay constant and the total number of radioactive nuclei present, providing a direct measure of the intensity of the radioactivity in a sample.

Decay Constant and Half-life

The decay constant is a parameter that quantifies the likelihood of a nucleus decaying per unit time, and it is inversely related to the half-life—the time it takes for half of the radioactive atoms to decay. This relationship, generally expressed as ? = ln(2)/half-life, is fundamental in predicting how a radioactive substance decays over time.

Isotopic Abundance and Mass Fraction

Isotopic abundance describes the relative amount of a particular isotope within an element. When combined with the mass fraction of the element in a compound or organism, it allows for the determination of how much of a specific isotope is present in a given mass, which is crucial when calculating the total number of radioactive atoms.

Mole Concept and Avogadro's Number

The mole concept bridges the gap between the macroscopic mass of a substance and the number of its constituent atoms by using Avogadro's number—the number of constituents in one mole of a substance. This conversion is vital for translating mass measurements into the number of atoms, an essential step in quantifying radioactive decay events.

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