NUC-10

Half-life

T_{1/2} = ln 2 / λ. Time for half the nuclei to decay.

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DecayHalf-life

Governing equation

T_{1/2}=\ln 2/\lambda

where

\lambda: Decay constant (1/s)
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-10 — Half-life) is the form associated with Half-life. Working symbols: $\lambda$ $\rightarrow$ $T_{1/2}$ . Independent of N. Related to mean life by T_{1/2} = τ ln 2.

Purpose

Purpose: compute

T_{1/2}

from

\lambda

in Nuclear physics via

T_{1/2}=\ln 2/\lambda

T_{1/2} = ln 2 / λ. Time for half the nuclei to decay. 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

\lambda = 0.010\,\mathrm{1/s}

, the governing relation

T_{1/2}=\ln 2/\lambda

yields

T_{1/2} = 69.315\,\mathrm{s}

. A staircase of remaining nuclei, a half tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Decay constant \lambda0.01 1/s

Outputs

Half-life T_{1/2}69.315 s

Reading speed

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Narration of this film

A staircase of remaining nuclei, a half tick.

Independent of N. Related to mean life by T_{1/2} = τ ln 2.

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