Nuclear Decay Chain Calculator

Radioactive isotopes don't just disappear — they transform through a chain of daughter products, each with its own decay rate. The Nuclear Decay Chain Calculator tracks this process: select a parent isotope (such as Uranium-238 or Cesium-137), enter your initial activity and activity unit, then set a time elapsed to see the remaining activity, decay constant, half-life, atoms remaining, and fraction decayed. Adjust decay steps to control how many generations of the chain are shown, or enable secular equilibrium for a full steady-state view.

Results

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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Results Table

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Frequently Asked Questions

What is radioactive decay?

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.

What is the activity of a radioactive substance?

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.

How do I calculate radioactive decay?

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.

What is a decay chain and how does it work?

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.

What is secular equilibrium in decay chains?

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.

Which measurement units are used for radioactivity?

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).

How do I calculate specific activity?

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.

What factors affect radioactive decay rates?

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.