NUC-03

Activity A = λ N

The expected number of decays per second. 1 Bq = 1 s⁻¹.

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DecaySI becquerel

Governing equation

A=\lambda N=\dfrac{\ln 2}{T_{1/2}}N

$T_{1/2} \in \left[1, 3\times 10^{7}\right]$

where

N: Nuclei (—)
T_{1/2}: Half-life (s)
A: Activity (Bq)

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.

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①

Governing law — red

A=\lambda N=\dfrac{\ln 2}{T_{1/2}}N

$T_{1/2} \in \left[1, 3\times 10^{7}\right]$

$T_{1/2} = 1$ $A = 6.93\times 10^{11}$

Along the curve

②

Domain of the variable — blue

T_{1/2}_{\min} = 1,\quad T_{1/2}_{\max} = 3\times 10^{7}

$T_{1/2} \in \left[1, 3\times 10^{7}\right]$

$T_{1/2} = 1$ $T_{1/2} = 1$

Along the curve

③

Response curve — green

A=\lambda N=\dfrac{\ln 2}{T_{1/2}}N

$T_{1/2} \in \left[1, 3\times 10^{7}\right]$

$T_{1/2} = 1$ $A = 6.93\times 10^{11}$

Along the curve

④

Rate of change — amber

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

$T_{1/2} \in \left[1, 3\times 10^{7}\right]$

$T_{1/2} = 1.89\times 10^{5}$ $A^{\prime} = -1.84\times 10^{6}$

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-03 — Activity A = λ N) is the form associated with SI becquerel. Working symbols: $N$ , $T_{1/2}$ $\rightarrow$ $A$ . Related to half-life by λ = ln2 / T½. Specific activity a = λ N_A / M for a pure isotope.

Purpose

Purpose: compute

A

from

N

T_{1/2}

in Nuclear physics via

A=\lambda N=\dfrac{\ln 2}{T_{1/2}}N

The expected number of decays per second. 1 Bq = 1 s⁻¹. 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

N = 1.000e+12\,\mathrm{—}

T_{1/2} = 3600.000\,\mathrm{s}

, the governing relation

A=\lambda N=\dfrac{\ln 2}{T_{1/2}}N

yields

A = 1.925e+8\,\mathrm{Bq}

. A sample, a Geiger tick rate. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Nuclei N1000000000000 —Half-life T_{1/2}3600 s

Outputs

Activity A192540883.489 Bq

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Narration of this film

A sample, a Geiger tick rate.

Related to half-life by λ = ln2 / T½. Specific activity a = λ N_A / M for a pure isotope.

Reading speed

Watch on YouTube