Enter your Parent Isotope, Initial Activity, and Time Elapsed to calculate the Remaining Activity, Atoms Remaining, and Fraction Decayed across each step in the chain — toggle Show Secular Equilibrium and adjust Number of Decay Steps to trace how daughter isotopes build up over time.
Remaining Activity
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Decay Constant
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Half-Life
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Atoms Remaining
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Fraction Decayed
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Radioactive decay is the spontaneous transformation of unstable atomic nuclei, releasing energy in the form of radiation. During this process, the parent nucleus transforms into a different element (daughter nucleus) by emitting particles like alpha, beta, or gamma rays.
Activity measures how many radioactive atoms decay per unit time in a sample. It's expressed in becquerels (Bq) in the SI system or curies (Ci) in the traditional system. One becquerel equals one decay per second, while one curie equals 3.7 × 10¹⁰ decays per second.
Radioactive decay follows the exponential decay law: N(t) = N₀ × e^(-λt), where N(t) is the number of atoms at time t, N₀ is the initial number, λ is the decay constant, and t is time. The activity A(t) = λN(t) follows the same exponential pattern.
A decay chain is a sequence of radioactive decays where each daughter nucleus is also unstable and decays further until reaching a stable isotope. For example, U-238 undergoes 14 decay steps through various elements before becoming stable Pb-206.
Secular equilibrium occurs in decay chains when the parent has a much longer half-life than its daughters. In this state, the rate of daughter production equals its decay rate, so the activity ratio remains constant over time.
The SI unit is the becquerel (Bq), equal to one decay per second. Traditional units include the curie (Ci), equal to 3.7 × 10¹⁰ Bq. Common prefixes include pico (pCi), nano (nCi), micro (μCi), milli (mCi), kilo (kBq), mega (MBq), and giga (GBq).
Specific activity is activity per unit mass, calculated as A/m = (λ × Nₐ)/M, where λ is the decay constant, Nₐ is Avogadro's number, and M is the atomic mass. It represents the activity of one gram of pure isotope.
Radioactive decay is a random quantum process with a fixed probability per unit time, characterized by the half-life. External factors like temperature, pressure, or chemical environment do not affect nuclear decay rates, making radioactive decay extremely reliable for dating and measurements.