Unlock the secrets of alpha decay with our Geiger Nuttall Law Calculator. Easily estimate an isotope's half-life and decay constant by inputting alpha particle energy, atomic number, and empirical constants. Perfect for students, researchers, and nuclear enthusiasts.
Formula:
The Geiger-Nuttall Law describes the empirical relationship between the half-life of an alpha-emitting radioactive isotope and the energy of the alpha particles emitted. A commonly used form of the law, relating the decay constant, is:
log₁₀(λ) = A - B × Z / √Eα
And the half-life is derived directly from the decay constant:
t₁/₂ = ln(2) / λ
- λ: Decay constant (in s⁻¹)
- A: Empirical constant (dimensionless)
- B: Empirical constant (in MeV½)
- Z: Atomic number of the parent nucleus (dimensionless)
- Eα: Alpha particle energy (in MeV)
- t₁/₂: Half-life (in seconds)
- ln(2): Natural logarithm of 2 (approximately 0.693)
Please note that the empirical constants A and B vary for different decay series, and typical values might be in the ranges of A ≈ 50-60 and B ≈ 1.5-2.0.