Nuclear Decay Chain Calculator

Choose a radioactive series to see the complete decay chain from parent to stable daughter. Trace alpha and beta transitions step by step on a cascade diagram or N-Z nuclide chart. Includes the three classic natural decay series plus a half-life and activity calculator.

Select Decay Series

αα (alpha)

β⁻β⁻ (beta minus)

β⁺β⁺ (beta plus)

γγ (gamma)

stableStable endpoint

Uranium Series (U-238 → Pb-206)14 decay steps · terminates at Pb-206 (stable)

8 α6 β⁻

Decay Cascade Diagram

Each box shows the isotope symbol with mass number (top-left) and atomic number (bottom-left). Colored arrows indicate the decay type. Half-life is shown to the right.

Reference Guide

Types of Radioactive Decay

Alpha decay (α)

The nucleus emits a helium-4 nucleus (2 protons, 2 neutrons). Mass number decreases by 4 and atomic number decreases by 2.

^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}He

Beta-minus decay (β⁻)

A neutron converts to a proton, emitting an electron and antineutrino. Mass number is unchanged; atomic number increases by 1.

^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + e^- + \bar{\nu}_e

Gamma decay (γ)

The nucleus releases energy as a high-energy photon without changing A or Z. Often follows alpha or beta decay when the daughter is in an excited state.

Decay Chains

Heavy nuclei rarely reach stability in a single step. Instead they undergo a sequence of decays called a decay chain (or decay series), each step producing a new isotope until a stable nucleus is reached.

The three natural decay series all terminate at lead isotopes, which have a "magic" proton number (Z = 82) conferring exceptional nuclear stability.

U-238 series: 8 alpha + 6 beta = Pb-206 (4.468 Gy)

U-235 series: 7 alpha + 4 beta = Pb-207 (703.8 My)

Th-232 series: 6 alpha + 4 beta = Pb-208 (14.05 Gy)

Each series conserves mass number modulo 4. U-238 and Th-234 have A = 4n + 2, U-235 has A = 4n + 3, Th-232 has A = 4n, which is why the series never cross.

Half-Life

The half-life t½ is the time for half the atoms in a sample to decay. After n half-lives, the fraction remaining is (1/2)^n.

N(t) = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}

Activity (decays per second) decreases at the same exponential rate. The decay constant λ relates to half-life by:

\lambda = \frac{\ln 2}{t_{1/2}}, \quad A = \lambda N

In a decay chain, short-lived intermediates quickly reach secular equilibrium with their long-lived parents, where each member has the same activity.

Nuclear Stability

Stable nuclei cluster along the "valley of stability" in the N-Z chart. Below the line (too few neutrons relative to protons), nuclei undergo beta-plus decay or electron capture. Above it (too many neutrons), they undergo beta-minus decay. Very heavy nuclei prefer alpha decay.

Nuclei with "magic numbers" of protons or neutrons (2, 8, 20, 28, 50, 82, 126) are particularly stable due to filled nuclear shells, analogous to noble gas electron configurations.

Lead-208 (Z = 82, N = 126) has both proton and neutron magic numbers, making it the heaviest truly stable isotope and the end-point of the thorium series.

Magic Z: 2, 8, 20, 28, 50, 82

Magic N: 2, 8, 20, 28, 50, 82, 126

Pb-208: Z = 82, N = 126 (doubly magic)