Radioactive Decay & Half-Life (A(t) = A₀ × (1/2)^(t / T₁/₂))

Input Parameters

Calculation Goal Guided Mode

Radionuclide Half-Life Presets Tc-99m (6.006 hr)

Nominal

Solved Value Updated automatically

Enter parameters on the left to calculate.

Geometry & Field Diagram Interactive Model

Sensitivity Curve

Remaining Activity (A) = Initial Activity (A₀) × exp(−ln(2) × Elapsed Time / Half-Life)

Symbol	Default Unit	Definition
A₀	Ci	Starting activity at calibration time t = 0.
A	Ci	Activity remaining after elapsed time t.
T₁/₂	s	Physical half-life of the radionuclide.
t	s	Elapsed decay duration between initial and final activity.

Decay constant λ = ln(2) / T₁/₂ ≈ 0.69315 / T₁/₂; mean lifetime τ = 1 / λ ≈ 1.4427 × T₁/₂.
After 7 half-lives, remaining activity drops to (1/2)⁷ = 1/128 ≈ 0.78% of initial activity.
After 10 half-lives, remaining activity is (1/2)¹⁰ = 1/1024 ≈ 0.098% (< 0.1%), the standard benchmark for decay-in-storage release of short-lived medical isotopes.