Nuclear Physics Formula Sheet

Core Equations of Nuclear Physics

These key mathematical models and conversion constants govern nuclear reactions and radiation safety:

\[_Z\text{X}^A \longrightarrow _{Z-2}\text{Y}^{A-4} + _2\text{He}^4\]

_Z\text{X}^A: Parent radioactive nucleus with atomic number \(Z\) and mass number \(A\)
_{Z-2}\text{Y}^{A-4}: Stable or unstable daughter nucleus with atomic number decreased by 2 and mass number decreased by 4
_2\text{He}^4: Alpha particle (helium nucleus) emitted during the disintegration

\[_Z\text{X}^A \longrightarrow _{Z+1}\text{Y}^A + _{-1}\text{e}^0\]

_Z\text{X}^A: Parent radioactive nucleus
_{Z+1}\text{Y}^A: Daughter nucleus with atomic number increased by 1 and unchanged mass number
_{-1}\text{e}^0: Beta particle (electron) ejected from the nucleus

\[_Z\text{X}^A \longrightarrow _Z\text{X}^A + \gamma\]

_Z\text{X}^A: Excited parent nucleus returning to a lower energy ground state
γ (gamma): Emitted high-energy electromagnetic photon, leaving atomic and mass numbers unchanged

\[E = mc^2\]

E: Energy equivalent of the mass defect in Joules (J)
m: Mass defect (difference between reactant and product masses) in kilograms (kg)
c: Velocity of light in vacuum, equal to \(3 \times 10^8\text{ m/s}\)

\[N = A - Z\]

\[1\text{ Curie (Ci)} = 3.7 \times 10^{10}\text{ disintegrations per second (Bq)}\]

\[1\text{ Rutherford (Rd)} = 10^6\text{ disintegrations per second (Bq)}\]

\[1\text{ Becquerel (Bq)} = 1\text{ disintegration per second}\]

Bq: The SI unit of radioactivity
Ci: The traditional unit of radioactivity, based on the activity of 1g of pure radium

\[1\text{ eV} = 1.602 \times 10^{-19}\text{ Joules (J)}\]

\[1\text{ MeV} = 10^6\text{ eV} = 1.602 \times 10^{-13}\text{ J}\]