NUC-12

Branching ratio

λ_i = b_i λ, A_i = b_i A. Partial width of one decay channel.

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DecayBranching

Governing equation

\lambda_i=b_i\lambda,\quad A_i=b_i A

$b_i \in \left[0, 1\right]$

where

A: Total activity (Bq)
b_i: Branching fraction (—)
A_i: Partial 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

\lambda_i=b_i\lambda,\quad A_i=b_i A

$b_i \in \left[0, 1\right]$

$b_i = 0$ $A_i = 0$

Along the curve

②

Domain of the variable — blue

b_i_{\min} = 0,\quad b_i_{\max} = 1

$b_i \in \left[0, 1\right]$

$b_i = 0$ $b_i = 0$

Along the curve

③

Response curve — green

\lambda_i=b_i\lambda,\quad A_i=b_i A

$b_i \in \left[0, 1\right]$

$b_i = 0$ $A_i = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}A_i}{\mathrm{d}b_i}

$b_i \in \left[0, 1\right]$

$b_i = 0.006$ $A_i^{\prime} = 1\times 10^{6}$

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-12 — Branching ratio) is the form associated with Branching. Working symbols: $A$ , $b_i$ $\rightarrow$ $A_i$ . Σ b_i = 1. Each channel is an independent Poisson process.

Purpose

Purpose: compute

A_i

from

A

b_i

in Nuclear physics via

\lambda_i=b_i\lambda,\quad A_i=b_i A

λ_i = b_i λ, A_i = b_i A. Partial width of one decay channel. 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 = 1.000e+6\,\mathrm{Bq}

b_i = 0.350\,\mathrm{—}

, the governing relation

\lambda_i=b_i\lambda,\quad A_i=b_i A

yields

A_i = 350000.00\,\mathrm{Bq}

. A fork of two decay arrows. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Total activity A1000000 BqBranching fraction b_i0.35 —

Outputs

Partial activity A_i350000.00 Bq

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Narration of this film

A fork of two decay arrows.

Σ b_i = 1. Each channel is an independent Poisson process.

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