AcademyNuclear Physics
Academy
Nuclear Stability
Level 1 - Physics topic page in Nuclear Physics.
Principle
Nuclear stability is set by energy lowering through binding, neutron balance, and allowed decay paths.
Notation
\(Q\)
decay or reaction energy release
J, MeV
\(B/A\)
binding energy per nucleon
MeV
\(N/Z\)
neutron-to-proton ratio
1
\(\alpha\)
helium-4 nucleus emitted in alpha decay
1
\(\beta^-\)
electron emission from neutron-rich nuclei
1
\(\beta^+\)
positron emission from proton-rich nuclei
1
Method
Derivation 1: Energy criterion
A decay can occur spontaneously only if final rest energy is lower.
Q value
\[Q=(m_{\mathrm i}-m_{\mathrm f})c^2\]
Spontaneous condition
\[Q>0\]
Derivation 2: Neutron balance
Stable heavy nuclei need extra neutrons to dilute proton repulsion.
Light stable trend
\[N\approx Z\]
Heavy stable trend
\[N>Z\]
Derivation 3: Direction of beta decay
Beta decay moves a nucleus toward a more stable neutron-proton balance.
Neutron rich
\[n\to p+e^-+\bar\nu_e\]
Proton rich
\[p\to n+e^++\nu_e\]
Rules
Q value
\[Q=(m_{\mathrm i}-m_{\mathrm f})c^2\]
Beta minus
\[^{A}_{Z}X\to\,^{A}_{Z+1}Y+e^-+\bar\nu_e\]
Beta plus
\[^{A}_{Z}X\to\,^{A}_{Z-1}Y+e^++\nu_e\]
Examples
Question
A neutron-rich nucleus beta decays. Does \(Z\) rise or fall?
Answer
In
\[\beta^-\]
decay, a neutron becomes a proton, so \(Z\) rises by 1.Checks
- Stability is not just large binding energy; compare available lower-energy states.
- Heavy stable nuclei usually have \(N/Z>1\).
- Alpha decay lowers both \(A\) and \(Z\).
- Beta decay changes \(Z\) but leaves \(A\) unchanged.