I'm afraid I'm suffering from a bit of brain block in try to get from the simple statement of change in the number of daughter nuclei arising from the decay of parent nuclei. The basic statement is straight forward...(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac {dN_d}{dt} = \lambda_pN_p - \lambda_dN_d

[/tex]

Subscripts d and p denote parent and daughter nuclei and lambda is the activity.

However I'm struggling to derive the following relationship from the above identity - I can't seem to find any pointers in any text books... At face value I think this should be a pretty easy first order ODE to solve, but I think I'm probably missing something blindingly obvious, but any tips would be gratefully recieved.

[tex]

N_d = \frac{\lambda_pN_{p0}}{\lambda_d - \lambda_p} (e^{-\lambda_pt}-e^{\lambda_dt}) + N_{d0}e^{\lambda_dt}

[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivation of Decay Chain Formulae

**Physics Forums | Science Articles, Homework Help, Discussion**