Vensim. System Dynamics. Vensim. System Thinking. System Dynamics. Vensim. System Thinking. System Dynamics. Vensim. System Thinking. Vensim

Boletín de Dinámica de Sistemas

Radon Decay Chain
A System Dynamics Based Model

Francesco Pagni

Dear reader, glad to be here!. This was my first autonomous exercise, using Vensim. It is similar to the famous tank exercise. We do have n tanks (n levels), corresponding to A, B, C,. box variables. The output of a tank is the input of the next one.

In this case, the box variable A represents the number of type "a" unstable (radioactive) atomic nucleus, B of type "b" and so on.

Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles (radiation).

Decay is said to occur in the parent nucleus and produces a daughter nucleus.

parent nucleus = daughter nucleus + radiation

In this case a = b+radiation, b= c+radiation and so on.

If one decay event occurs the number of parent nucleus decreases by 1 and the number of daughter nucleus increases by 1. In the case a=b+radiation, A= A-1 and B= B+1. The variation of the level B versus time dB/dt [number/second] is equal to the disintegration per second of radionuclide "a" [number/second] minus the disintegration of radionuclide "b" itself [number/second].

The generic causal loop diagram describing decay is:

Radon Decay Chain

The flow diagram is (N is the number of doughter nuclei, N0 is its initial value, "Parent dps" is the number of parent decay events per second and "Daughter dps" is the number of daughter decay events per second).

Please, programme the flow diagram using Vensim and run the model in the case the radionuclide has not a parent (Parent dps=0 second-1). You'll discover the famous exponential rule

N(t)=N0 exp(-ln(2)*t/DoughterHalfLife)

You should obtain following results.

Radon Decay Chain

Let us play with a simplified version of Radon 222 decay chain.

Radon-222 is a chemically inert gas emanating from the soil and stone; it diffuses through the air and decays with the emission of an alpha particle.The decay chain of Radon-222 contains seven radioactive nuclides and one stable nuclide. Let us take only 3 of them:

Rn-222, (T0=3.8 days) =..= Pb-214 (T2=26.8 min) = .. = Pb-210 (22 yr)

The flow diagram can be built cloning the "Decay cell" described before and linking clones together.

Online Courses               

Building System Dynamics Simulation Models

Advanced Course in
System Dynamics

Building Models in Natural Resources Management

Advanced Course Universitat Politècnica de Catalunya


System Dynamics

System Dynamics

System Dynamics


  • 1993 Cancun, Mexico
  • 1994 Stirling, Scotland
  • 1995 Tokyo, Japan
  • 1996 Cambridge, MA, USA
  • 1997 Istanbul, Turkey
  • 1998 Quebec City,Canada
  • 1999 Wellington, New Zealand
  • 2000 Bergen, Norway
  • 2001 Atlanta, Georgia, USA
  • 2002 Palermo, Italy
  • 2003 New York City, USA
  • 2004 Oxford, England
  • 2005 Boston, MA, USA
  • 2006 Nijmegen, The Netherlands
  • 2007 Boston, MA, USA
  • 2008 Athens, Greece
  • 2009 Albuquerque, USA
  • 2010 Seoul, Korea
  • 2011 Washington, DC, USA
  • 2012 St. Gallen, Switzerland
  • 2013 Cambridge, MA, USA
  • 2014 The Delf, Netherlands
  • 2015 Cambridge, MA, USA
  • Google
    Home     Information

    System Dynamics. Vensim. System Dynamics. Vensim. System Dynamics. Vensim. System Dynamics. Vensim. System Dynamics. Vensim.