Key Equations

Key Equations

Atomic mass number	$A=Z+N$
Standard format for expressing an isotope	${}_Z^A\text{X}$
Nuclear radius, where r0 is the radius of a single proton	$r=r_0{A}^{1\text{/}3}$
Mass defect	$\text{Δ}m=Z{m}_p+(A-Z)m_n-m_{\text{nuc}}$
Binding energy	$E=(\text{Δ}m)c^2$
Binding energy per nucleon	$BEN=\frac{E_b}{A}$
Radioactive decay rate	$-\frac{dN}{dt}=\lambda N$
Radioactive decay law	$N=N_0{e}^{\text{−}\lambda t}$
Decay constant	$\lambda =\frac{0.693}{T_{1\text{/}2}}$
Lifetime of a substance	$\bar{T}=\frac{1}{\text{λ}}$
Activity of a radioactive substance	$A=A_0{e}^{\text{−}\lambda t}$
Activity of a radioactive substance (linear form)	$\text{ln}A=\text{−}\lambda t+\text{ln}{A}_0$
Alpha decay	${}_Z^A\text{X}\to {}_{Z-2}^{A-4}\text{X}+{}_2^4\text{H}\text{e}$
Beta decay	${}_Z^A\text{X}\to {}_{Z+1}^A\text{X}+{}_{\mathrm{-1}}^0\text{e}\text{+}\bar{v}$
Positron emission	${}_Z^A\text{X}\to {}_{Z-1}^A\text{X}+{}_{\text{+}1}^0\text{e}\text{+}v$
Gamma decay	${}_Z^A\text{X}*\to {}_Z^A\text{X}+\gamma$