Decay Series Calculator

Calculate radioactive decay series, half-lives, and decay products. Understand nuclear decay processes.

Single Nuclide
Decay Series
Radiometric Dating
Activity Calculator
For predefined nuclides, half-life is automatically set
s⁻¹
Calculated from half-life
For predefined methods, half-life is automatically set
Amount of daughter nuclide present at time zero
Bq/g
Calculated activity per gram
MeV
For predefined nuclides
Calculating...
Decay Calculation Results

Understanding Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process transforms the original nuclide into a different nuclide, which may be stable or continue to decay further.

Key Concept: The rate of radioactive decay is characterized by the half-life, which is the time required for half of the radioactive atoms in a sample to decay.

Types of Radioactive Decay

1

Alpha Decay (α): Emission of an alpha particle (helium nucleus: 2 protons and 2 neutrons). Decreases atomic number by 2 and mass number by 4.

2

Beta Decay (β): Transformation of a neutron into a proton (β⁻) or a proton into a neutron (β⁺). Changes atomic number by ±1 while mass number remains the same.

3

Gamma Decay (γ): Emission of high-energy photons from an excited nucleus. Does not change the atomic or mass number, only reduces energy state.

4

Electron Capture: Capture of an inner orbital electron by the nucleus, converting a proton to a neutron. Decreases atomic number by 1.

Common Radioactive Decay Series

Decay Series Parent Nuclide Stable End Product Half-Life of Parent Number of Steps
Uranium Series U-238 Pb-206 4.468 billion years 14
Actinium Series U-235 Pb-207 704 million years 11
Thorium Series Th-232 Pb-208 14.05 billion years 10
Neptunium Series Np-237 Bi-209 2.14 million years 11

Decay Formulas

Fundamental equations used in radioactive decay calculations:

  • Decay Law: N(t) = N₀ × e^(-λt)
  • Half-Life Relation: T½ = ln(2) / λ
  • Activity: A(t) = λ × N(t)
  • Dating Formula: t = (1/λ) × ln(1 + D/P)

Where:
N(t) = number of atoms at time t
N₀ = initial number of atoms
λ = decay constant
T½ = half-life
A(t) = activity at time t
D = daughter nuclide amount
P = parent nuclide amount

Safety Note: Radioactive materials emit ionizing radiation that can be harmful to living tissue. Always follow proper safety protocols when handling radioactive substances.

Frequently Asked Questions

Half-life (T½) is the time required for half of the radioactive atoms in a sample to decay. Decay constant (λ) is the probability per unit time that a given atom will decay. They are related by the formula T½ = ln(2) / λ. Half-life is more intuitive for understanding decay rates, while the decay constant is more useful in mathematical calculations.

Radiometric dating can be highly accurate when properly applied. The accuracy depends on several factors: knowledge of the initial conditions, whether the system has remained closed (no loss or gain of parent or daughter isotopes), precise measurement of isotope ratios, and accurate half-life values. Different methods are suitable for different time ranges - carbon-14 dating is useful for materials up to about 50,000 years old, while uranium-lead dating can date rocks billions of years old with precision of 1-2%.

Secular equilibrium occurs in a radioactive decay series when the half-life of the parent nuclide is much longer than any of the daughter nuclides. After enough time has passed, each daughter nuclide decays at the same rate it is produced, resulting in constant activity ratios between all members of the series. This state is typically reached after about 10 half-lives of the longest-lived daughter nuclide.

1 Curie (Ci) = 3.7 × 10¹⁰ Becquerel (Bq)
1 Becquerel (Bq) = 2.7 × 10⁻¹¹ Curie (Ci)

The Curie is based on the activity of 1 gram of radium-226, while the Becquerel is the SI unit of activity, defined as one disintegration per second. For practical purposes:
• 1 mCi (millicurie) = 37 MBq (megabecquerel)
• 1 μCi (microcurie) = 37 kBq (kilobecquerel)

Radioactive decay rates are generally constant and unaffected by external conditions like temperature, pressure, or chemical environment. This principle is fundamental to radiometric dating. However, there are a few exceptional cases:
• Electron capture rates can be slightly affected by chemical environment
• In certain special conditions, extreme pressure might slightly affect decay rates
• Bound beta decay can occur in fully ionized atoms
For virtually all practical purposes, decay rates can be considered constant and predictable.