Radioactive Decay

Simple Decay Tool

The HPS has a very simple radioactive decay tool on their new site.
Decay Calculator

Bateman Equation

For more complex decay of radioactive material with radioactive progeny the Bateman equation is more appropriate.
$N_n(t)=N_1(0)\times \left(\prod _{i=1}^{n-1}{\lambda }_i\right)\times \sum _{i=1}^n\frac{e^{-{\lambda }_{i}t}}{\prod _{j=1,j\ne i}^n({\lambda }_j-{\lambda }_i)}$

Universal Decay Calculator

The WISE Uranium Project has a calculator which performs the Bateman equation with minimal user input and visualizes the resulting activities in their different equilibrium.
Universal Decay Calculator
Despite being an anti-nuclear organization, the calculator is quite nice.

Example Equation

DRAFT - Not Finished

A nuclear medicine department receives a 10 Ci generator of Mo99 which was pure when shipped from the supplier 24 hours ago. Assuming no extractions have occured, how much Tc-99m is present in the generator now.

Isotopes

$Isotop{e}_0=Mo99$

$Isotop{e}_1=Tc99m$

$Isotop{e}_2=Tc99$

Half Life

T_1/2 of Mo99 is 65.924 hours

T_1/2 of Tc99m is 6.0072 hours

T_1/2 of Tc99 is 2.111E5 years

Decay Constant

${\lambda }_0=\frac{ln(2)}{65.924hr}=$

${\lambda }_1=\frac{ln(2)}{6.0072hr}=$

${\lambda }_2=\frac{ln(2)}{\frac{2.111E5yr}{}*\frac{365.25d}{1yr}*\frac{24h}{1d}}=$

Initial Activity

$N_0(0)=10Ci$

$N_1(0)=0Ci$

$N_2(0)=0Ci$

$N_n(t)=N_1(0)\times \left(\prod _{i=1}^{n-1}{\lambda }_i\right)\times \sum _{i=1}^n\frac{e^{-{\lambda }_{i}t}}{\prod _{j=1,j\ne i}^n({\lambda }_j-{\lambda }_i)}$