NUC-05

Fission energy (Coulomb snapshot)

E ≈ 1.44 Z₁ Z₂ / (A₁^{1/3}+A₂^{1/3}) MeV. Coulomb energy of two fragments at contact.

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NuclearFission

Governing equation

E\approx\dfrac{1.44\,Z_1 Z_2}{A_1^{1/3}+A_2^{1/3}}\,\mathrm{MeV}

$Z_1 \in \left[20, 60\right]$

where

Z_1: Z light (—)
A_1: A light (—)
Z_2: Z heavy (—)
A_2: A heavy (—)
E: Fission energy (MeV)

The figure, part by part

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①

Governing law — red

E\approx\dfrac{1.44\,Z_1 Z_2}{A_1^{1/3}+A_2^{1/3}}\,\mathrm{MeV}

$Z_1 \in \left[20, 60\right]$

$Z_1 = 20$ $E = 165.5$

Along the curve

②

Domain of the variable — blue

Z_1_{\min} = 20,\quad Z_1_{\max} = 60

$Z_1 \in \left[20, 60\right]$

$Z_1 = 20$ $Z_1 = 20$

Along the curve

③

Response curve — green

E\approx\dfrac{1.44\,Z_1 Z_2}{A_1^{1/3}+A_2^{1/3}}\,\mathrm{MeV}

$Z_1 \in \left[20, 60\right]$

$Z_1 = 20$ $E = 165.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}Z_1}

$Z_1 \in \left[20, 60\right]$

$Z_1 = 20.25$ $E^{\prime} = 8.277$

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-05 — Fission energy (Coulomb snapshot)) is the form associated with Fission. Working symbols: $Z_1$ , $A_1$ , $Z_2$ , $A_2$ $\rightarrow$ $E$ . A pedagogical stand-in for the ~200 MeV of ²³⁵U. Most of the Q is Coulomb, not surface.

Purpose

Purpose: compute

E

from

Z_1

A_1

Z_2

A_2

in Nuclear physics via

E\approx\dfrac{1.44\,Z_1 Z_2}{A_1^{1/3}+A_2^{1/3}}\,\mathrm{MeV}

E ≈ 1.44 Z₁ Z₂ / (A₁^{1/3}+A₂^{1/3}) MeV. Coulomb energy of two fragments at contact. 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

Z_1 = 36.000\,\mathrm{—}

A_1 = 95.000\,\mathrm{—}

Z_2 = 56.000\,\mathrm{—}

A_2 = 139.000\,\mathrm{—}

, the governing relation

E\approx\dfrac{1.44\,Z_1 Z_2}{A_1^{1/3}+A_2^{1/3}}\,\mathrm{MeV}

yields

E = 298.0\,\mathrm{MeV}

. A drop that splits, two charged fragments. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Z light Z_136 —A light A_195 —Z heavy Z_256 —A heavy A_2139 —

Outputs

Fission energy E298.0 MeV

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Narration of this film

A drop that splits, two charged fragments.

A pedagogical stand-in for the ~200 MeV of ²³⁵U. Most of the Q is Coulomb, not surface.

Reading speed

Watch on YouTube