NUC-26

Delayed-neutron reactivity

ρ = (k−1)/k, $ = ρ/β. Dollars of reactivity in units of the delayed fraction β.

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NuclearDelayed neutrons

Governing equation

\rho=(k-1)/k,\quad \$=\rho/\beta

where

k: Multiplication k (—)
\beta: Delayed fraction (—)
\rho: Reactivity (pcm)
\$: Dollars ($)

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-26 — Delayed-neutron reactivity) is the form associated with Delayed neutrons. Working symbols: $k$ , $\beta$ $\rightarrow$ $\rho$ , $\$ $. Prompt critical is ρ = β. Delayed neutrons make reactors controllable.

Purpose

Purpose: compute

\rho

\

from

,

\beta

in Nuclear physics via

\rho=(k-1)/k,\quad \

=\rho/\beta $

ρ = (k−1)/k,

= ρ/β. Dollars of reactivity in units of the delayed fraction β. 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

k = 1.001\,\mathrm{—}

\beta = 0.006\,\mathrm{—}

, the governing relation

\rho=(k-1)/k,\quad \$=\rho/\beta

yields

\rho = 99.9\,\mathrm{pcm}

\

= 0.154\,\mathrm{}$. A k needle, a β band, a dollar mark. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Multiplication k k1.001 —Delayed fraction \beta0.0065 —

Outputs

Reactivity \rho99.9 pcm
Dollars \$0.154 $

Reading speed

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Narration of this film

A k needle, a β band, a dollar mark.

Prompt critical is ρ = β. Delayed neutrons make reactors controllable.

Reading speed

Watch on YouTube