Half-Life and Radioactive Decay Calculator
Calculate the remaining quantity of a radioactive substance, its activity, decay constant, or elapsed time using the radioactive decay law.
Results will appear here.
Formulas Used
Radioactive Decay Law: N(t) = N₀ · e−λt
Decay Constant: λ = ln(2) / t½ ≈ 0.693147 / t½
Half-Life from measurements: t½ = −t · ln(2) / ln(N/N₀)
Elapsed Time: t = −t½ · ln(N/N₀) / ln(2)
Initial Quantity: N₀ = N · eλt
Activity: A = λ · N (in Becquerels when N is in atoms)
Mean Lifetime: τ = 1/λ = t½ / ln(2)
Assumptions & References
- Reference: Rutherford, E. & Soddy, F. (1902). "The Cause and Nature of Radioactivity." Philosophical Magazine.
- Reference: Bateman, H. (1910). "Solution of a system of differential equations." Proc. Cambridge Phil. Soc.