Radioactive Decay Calculator

Radioactive decay follows first-order exponential kinetics, meaning the rate of decay is directly proportional to the number of radioactive atoms present. The fundamental equation relating total activity (A) to the mass of the substance is expressed as Activity = (mass / molar mass) * Avogadro's number * (ln(2) / half-life). Furthermore, the specific activity, which measures the radioactivity per unit mass, is calculated using the formula specific activity = (Avogadro's number / molar mass) * (ln(2) / half-life). Here, ln(2) represents the natural logarithm of 2 (approximately 0.693), and Avogadro's number (Na) is approximately 6.022 x 10^23 mol^-1.

Let us calculate the activity of a 2-gram sample of Carbon-14. First, identify the known variables: the mass is 2 g, the molar mass of Carbon-14 is 14 g/mol, the half-life of Carbon-14 is approximately 5,730 years (or about 1.808 x 10^11 seconds for SI unit consistency), and Avogadro's number is 6.022 x 10^23. Substituting these values into our equation, we first find the moles of the substance by dividing 2 g by 14 g/mol, yielding 0.1428 moles. Next, multiply this by Avogadro's number to find the total number of atoms. Finally, multiply by the decay constant (ln(2) divided by the half-life in seconds) to arrive at the total radioactive activity in Becquerels (disintegrations per second).

Always ensure your time units are consistent before running calculations; converting half-lives from years or days into seconds is a common requirement when working with standard SI units like Becquerels. Double-check your molar mass values, especially when dealing with specific radioactive isotopes rather than naturally occurring elemental averages. Keep in mind that specific activity is an intensive property unique to the isotope, whereas total activity depends heavily on the total mass of the sample.