Key Equations

Atomic mass number	$A = Z + N$
Standard format for expressing an isotope	$_{Z}^{A} X$
Nuclear radius, where r₀ is the radius of a single proton	$r = r_{0} A^{1 / 3}$
Mass defect	$Δ m = Z m_{p} + (A - Z) m_{n} - m_{nuc}$
Binding energy	$E = (Δ m) c^{2}$
Binding energy per nucleon	$B E N = \frac{E_{b}}{A}$
Radioactive decay rate	$- \frac{d N}{d t} = λ N$
Radioactive decay law	$N = N_{0} e^{− λ t}$
Decay constant	$λ = \frac{0.693}{T_{1 / 2}}$
Lifetime of a substance	$\bar{T} = \frac{1}{λ}$
Activity of a radioactive substance	$A = A_{0} e^{− λ t}$
Activity of a radioactive substance (linear form)	$ln A = − λ t + ln A_{0}$
Alpha decay	$_{Z}^{A} X \to_{Z - 2}^{A - 4} X +_{2}^{4} H e$
Beta decay	$_{Z}^{A} X \to_{Z + 1}^{A} X +_{−1}^{0} e + \bar{v}$
Positron emission	$_{Z}^{A} X \to_{Z - 1}^{A} X +_{+ 1}^{0} e + v$
Gamma decay	$_{Z}^{A} X * \to_{Z}^{A} X + γ$