NUC-24

Nuclear radius

R = R₀ A^{1/3}. The liquid-drop size of a nucleus.

Reading speed

NuclearNuclear radius

Governing equation

R=R_0 A^{1/3}

$A \in \left[1, 240\right]$

where

R_0: r₀ (fm)
A: Mass number (—)
R: Radius (fm)

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.

00:0 / 00:08

①

Governing law — red

R=R_0 A^{1/3}

$A \in \left[1, 240\right]$

$A = 1$ $R = 1.2$

Along the curve

②

Domain of the variable — blue

A_{\min} = 1,\quad A_{\max} = 240

$A \in \left[1, 240\right]$

$A = 1$ $A = 1$

Along the curve

③

Response curve — green

R=R_0 A^{1/3}

$A \in \left[1, 240\right]$

$A = 1$ $R = 1.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R}{\mathrm{d}A}

$A \in \left[1, 240\right]$

$A = 2.503$ $R^{\prime} = 0.235$

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-24 — Nuclear radius) is the form associated with Nuclear radius. Working symbols: $R_0$ , $A$ $\rightarrow$ $R$ . R₀ ≈ 1.2 fm from electron scattering. Density is nearly constant inside.

Purpose

Purpose: compute

R

from

R_0

A

in Nuclear physics via

R=R_0 A^{1/3}

R = R₀ A^{1/3}. The liquid-drop size of a nucleus. 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

R_0 = 1.200\,\mathrm{fm}

A = 56.000\,\mathrm{—}

, the governing relation

R=R_0 A^{1/3}

yields

R = 4.591\,\mathrm{fm}

. A growing drop labelled by A. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

r₀ R_01.2 fmMass number A56 —

Outputs

Radius R4.591 fm

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A growing drop labelled by A.

R₀ ≈ 1.2 fm from electron scattering. Density is nearly constant inside.

Reading speed

Watch on YouTube