NUC-22

Geiger–Nuttall law

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

Reading speed

DecayGeiger–Nuttall

Governing equation

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

$Q \in \left[3, 10\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

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

$Q \in \left[3, 10\right]$

$Q = 3$ $T_{1/2} = 6.75\times 10^{28}$

Along the curve

②

Domain of the variable — blue

Q_{\min} = 3,\quad Q_{\max} = 10

$Q \in \left[3, 10\right]$

$Q = 3$ $Q = 3$

Along the curve

③

Response curve — green

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

$Q \in \left[3, 10\right]$

$Q = 3$ $T_{1/2} = 6.75\times 10^{28}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}T_{1/2}}{\mathrm{d}Q}

$Q \in \left[3, 10\right]$

$Q = 3.044$ $T_{1/2}^{\prime} = -7.13\times 10^{29}$

Along the curve

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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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