Beta Decay Calculator
Calculate nuclear binding energy ΔE = Δm c², radioactive decay N(t) = N₀ e^(-λt), half-life t_1/2, mass defect, and radiation shielding for beta decay.
Input Nuclear Parameters
Enter initial isotope quantity N₀, half-life t_1/2, or mass defect Δm.
Remaining Radioactive Quantity N(t)
Radioactive Decay Law
N(t) = N₀ × (1/2)^(t / t_1/2) = N₀ × e^(-λt). After two half-lives (t = 2 × t_1/2), exactly 25% of the original parent isotope sample remains.
Calculation Methodology & Details
Formula
Applies atomic mass unit equivalences (1 u = 931.494 MeV), semi-empirical liquid drop mass formulas, and linear radiation attenuation coefficients.
Important Disclaimer
Nuclear binding energy calculations use rest masses of protons (1.007276 u), neutrons (1.008665 u), and neutral isotope atomic masses in atomic mass units (u).
How to Calculate Step-by-Step
Follow these steps to complete the calculation:
Step 1
Enter initial radioactivity N₀ (Becquerels/Curies) or atomic mass defect Δm in amu.
Step 2
Input isotope half-life t_1/2 and elapsed decay time t.
Step 3
View remaining activity N(t), total nuclear binding energy in MeV, Q-value of nuclear fission/fusion reactions, or lead shielding thickness.
Detailed Insights & Expert Guide
ℹ️ About this Calculation
The Beta Decay Calculator calculates mass defect Δm, total and per-nucleon nuclear binding energy E_b, radioactive half-life decay curves, nuclear reaction Q-values, Becquerel to Curie conversions, and radiation shielding thickness.
Variable Glossary
Half-Life (t_1/2)
Time required for half of the radioactive nuclei in a sample to undergo decay (t_1/2 = ln(2) / λ).
Binding Energy (E_b)
Energy required to completely disassemble a atomic nucleus into individual constituent protons and neutrons (MeV).