NUC-22

Geiger–Nuttall law

log₁₀ T_{1/2} = a + b / √Q. α half-life versus decay energy.

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DecayGeiger–Nuttall

Governing equation

\log_{10}T_{1/2}=a+b/\sqrt{Q}

where

a: Intercept a (—)
b: Slope b (MeV^{1/2})
Q: α energy (MeV)
T_{1/2}: Half-life (s)

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-22 — Geiger–Nuttall law) is the form associated with Geiger–Nuttall. Working symbols: $a$ , $b$ , $Q$ $\rightarrow$ $T_{1/2}$ . A logarithmic image of the Gamow factor. Even–even nuclei share (a,b) roughly.

Purpose

Purpose: compute

T_{1/2}

from

a

b

Q

in Nuclear physics via

\log_{10}T_{1/2}=a+b/\sqrt{Q}

log₁₀ T_{1/2} = a + b / √Q. α half-life versus decay energy. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = -52.000\,\mathrm{—}

b = 140.000\,\mathrm{MeV^1/2}

Q = 5.000\,\mathrm{MeV}

, the governing relation

\log_{10}T_{1/2}=a+b/\sqrt{Q}

yields

T_{1/2} = 4.073e+10\,\mathrm{s}

. A log-lifetime versus 1/√Q line. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Intercept a a-52 —Slope b b140 MeV^{1/2}α energy Q5 MeV

Outputs

Half-life T_{1/2}40728964625.971 s

Reading speed

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Narration of this film

A log-lifetime versus 1/√Q line.

A logarithmic image of the Gamow factor. Even–even nuclei share (a,b) roughly.

Reading speed

Watch on YouTube