AcademyNuclear Physics
Academy
Nuclear Properties
Level 1 - Physics topic page in Nuclear Physics.
Principle
Nuclear properties are organized by proton number, neutron number, mass defect, radius, and charge.
Notation
\(Z\)
proton number
1
\(N\)
neutron number
1
\(A\)
nucleon number
1
\(R\)
nuclear radius
\(\mathrm{m}\)
\(u\)
atomic mass unit
\(\mathrm{kg}\)
\(e\)
elementary charge
\(\mathrm{C}\)
Method
Derivation 1: Nuclide bookkeeping
The nuclide symbol stores composition.
Mass number
\[A=Z+N\]
Neutron number
\[N=A-Z\]
Nuclear charge
\[q=+Ze\]
Derivation 2: Nuclear size
Nearly constant nuclear density gives a radius proportional to the cube root of nucleon number.
Volume scaling
\[\frac{4}{3}\pi R^3\propto A\]
Radius law
\[R=R_0A^{1/3}\]
Derivation 3: Density scale
Using \(m_{\mathrm N}\approx u\) gives the nuclear density scale.
Mass estimate
\[M\approx Au\]
Density estimate
\[\rho\approx\frac{Au}{(4/3)\pi R_0^3A}=\frac{3u}{4\pi R_0^3}\]
Rules
Nucleon count
\[A=Z+N\]
Nuclear radius
\[R=R_0A^{1/3}\]
Nuclear density
\[\rho\approx\frac{3u}{4\pi R_0^3}\]
Examples
Question
Find \(N\) for
\[^{238}_{92}\mathrm U\]
Answer
\[N=A-Z=238-92=146\]
Checks
- Isotopes have the same \(Z\) and different \(N\).
- Nuclear charge depends on \(Z\), not \(A\).
- Nuclear mass is close to \(Au\), but binding energy changes it.
- Radius grows slowly because it scales as \(A^{1/3}\).