NUC-02

Binding energy per nucleon (sketch)

B/A ≈ a_v − a_s A^{−1/3} − a_c Z² A^{−4/3}. The Weizsäcker sketch without pairing/asymmetry.

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DecaySEM

Governing equation

B/A=a_v-a_s A^{-1/3}-a_c Z^2 A^{-4/3}

$A \in \left[12, 240\right]$

where

A: Mass number (—)
Z: Atomic number (—)
B/A: Binding per nucleon (MeV)

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

B/A=a_v-a_s A^{-1/3}-a_c Z^2 A^{-4/3}

$A \in \left[12, 240\right]$

$A = 12$ $B/A = -9.762$

Along the curve

②

Domain of the variable — blue

A_{\min} = 12,\quad A_{\max} = 240

$A \in \left[12, 240\right]$

$A = 12$ $A = 12$

Along the curve

③

Response curve — green

B/A=a_v-a_s A^{-1/3}-a_c Z^2 A^{-4/3}

$A \in \left[12, 240\right]$

$A = 12$ $B/A = -9.762$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}B/A}{\mathrm{d}A}

$A \in \left[12, 240\right]$

$A = 13.43$ $B/A^{\prime} = 1.715$

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-02 — Binding energy per nucleon (sketch)) is the form associated with SEM. Working symbols: $A$ , $Z$ $\rightarrow$ $B/A$ . Volume term, surface deficit, Coulomb penalty. The iron peak sits near A = 56.

Purpose

Purpose: compute

B/A

from

A

Z

in Nuclear physics via

B/A=a_v-a_s A^{-1/3}-a_c Z^2 A^{-4/3}

B/A ≈ a_v − a_s A^{−1/3} − a_c Z² A^{−4/3}. The Weizsäcker sketch without pairing/asymmetry. 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 = 56.000\,\mathrm{—}

Z = 26.000\,\mathrm{—}

, the governing relation

B/A=a_v-a_s A^{-1/3}-a_c Z^2 A^{-4/3}

yields

B/A = 8.764\,\mathrm{MeV}

. A drop of nuclear fluid, a B/A curve. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass number A56 —Atomic number Z26 —

Outputs

Binding per nucleon B/A8.764 MeV

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Narration of this film

A drop of nuclear fluid, a B/A curve.

Volume term, surface deficit, Coulomb penalty. The iron peak sits near A = 56.

Reading speed

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