Decay Particle

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Default-person Stina Krist (Author)

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Child of model Decay preview imageDecay
Model group LS426-2012 | Visible to everyone | Changeable by group members (LS426-2012)
Model was written in NetLogo 5.0RC7 • Viewed 223 times • Downloaded 7 times • Run 0 times
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REFLECTION

When exploring the models, we both found it pretty easy to see how the models worked and why. The documentation seemed to do a good job of explaining the individual level behaviors, and we could investigate the higher level behavior with the model. In some cases, the extension questions really tested our understanding of the model, like with the predation model. In other cases, we seemed to be able to answer the questions without any further investigation.

We extended the model by having the decayed particles shoot out a new particle (i.e. create a new red turtle). When these emitted particles hit a nuclei, that nuclei decays. We can see a chain reaction appear when we set the chance of decay low and watch how the red (emitted) particles cause the blue ones to decay. In these cases, the decay rate steadily grows, reaches a peak, and then decreases.

While extending with model, we learned how to create new turtles and how to get two turtles to interact (i.e. have one turtle check to see if it has any neighbors and then have the neighbor do something).

WHAT IS IT?

This model simulates the spontaneous decay of a collection of radioactive nuclei. As they decay and become stable, the plot of the number that are still radioactive demonstrates the notion of "half-life". When each nuclei decays, it releases a particle that interacts with nuclei that are still radioactive, initiating decay.

HOW IT WORKS

At each time tick, each undecayed (light blue) nucleus has a certain chance of decaying. When a nucleus decays, it briefly flashes bright yellow (as if giving off radiation), then turns dark blue. Eventually, if you wait long enough, all of the nuclei will have decayed and the model will stop.

HOW TO USE IT

Set the initial number of nuclei (NUMBER-NUCLEI slider) and the likelihood of decay during each time interval (DECAY-CHANCE slider). Then push the SETUP button. Push the GO button to run the model.

The number of radioactive nuclei that remain is shown in the "Radioactive Nuclei" plot. Each time the number of nuclei is reduced by half, red and green lines appear on the plot to mark the place where each halfway mark was reached. The "Decay Rate" plot shows the number of decays that occur during each clock tick.

THINGS TO NOTICE

What is the shape of the decay curve (Radioactive Nuclei)? How is this affected by the initial conditions?

Why is the decay curve this shape? Is it the same as the decay curve shown in books?

The time between red lines is called the half-life. What is its physical meaning? Is it constant as the number of nuclei decreases? Is it affected by the initial number of nuclei or the decay-chance? Do you think it's a useful way to characterize a radioactive material?

How long does it take for all the nuclei to decay?

Watch one nucleus carefully. When will it decay?

Radioactivity depends on the number of decays per unit time (Decay Rate), because each decay event gives off radiation. What happens to the radioactivity of this sample over time? What is the shape of the decay rate curve? How is it related to the shape of the decay curve?

Examine the standard equation for nuclear decay:

N = No (e exp -(T/tau))

No is the initial number of nuclei, N is the number at a later time T, and tau is the "mean lifetime". Compare its behavior to what you see in this model. The corresponding equation for radiation is:

R = Ro (e exp -(T/tau))

Why are these two equations so similar?

THINGS TO TRY

Try the extremes of the initial conditions: many or few nuclei, high or low decay-chance. How does this affect the "jaggedness" of the decay rate plot?

What does the plot do when very few nuclei are left?

What instructions would you give each turtle be to make it behave like an unstable nucleus? Check the code in the Code tab and see if it's what you thought it should be.

Carbon-14 dating involves comparing the ratio of a stable (C-12) to an unstable (C-14) nucleus. Explain that method in terms of this model.

EXTENDING THE MODEL

It is often the case in nature that two nuclei with different decay rates are present in the same sample. Modify this model to have two or more types of nuclei. What happens to the radiation curve?

In this model, the nuclei don't affect their neighbors when they decay --- they just disappear. Get them to emit particles that in turn cause reactions in other nuclei. See if you can model a chain reaction. (See the Reactor Top Down and Reactor X-Section models.)

RELATED MODELS

  • Reactor Top-Down
  • Reactor X-Section

HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

COPYRIGHT AND LICENSE

Copyright 1997 Uri Wilensky.

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.

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Click to Run Model

globals [
  decays       ;; # of decays during this tick
  last-count   ;; this is the number of nuclei at the beginning --
]              ;; reset each time a red line is drawn on the plot

to setup
  clear-all
  set-default-shape turtles "circle"
  ask n-of number-nuclei patches [
    sprout 1 [ set color cyan ] 
    ]
  set last-count number-nuclei    ;; remember the starting number of nuclei
  set decays 0
  reset-ticks
end 

to go
  ;; if all the nuclei have decayed then stop the model
  if not any? turtles with [color = cyan]
    [ stop ]
  set decays 0
    ask turtles with [ color = red ]
    [ifelse any? other turtles-here with [ color = cyan ]
      [ ask one-of other turtles-here [ glow ] 
        die ]
    [ fd 1 ]     
    ]
    
  ask turtles with [ color = cyan ] [
    if random-float 100.0 < decay-chance
        [ glow ] 
    ] 
  display  ;; so the user sees the yellow
  ask turtles with [color = yellow]
    [ set color blue - 3 ]
  tick
end 

to glow
  set color yellow
  set decays decays + 1
  rt (random 360)
  hatch 1 [
  set color red 
  fd 1 
  ]
end 

;;from the code that is now in react
;to test
;  ask target [ glow ]
;       die ]
;      [fd 1]
;end

;to communicate
;  ask turtles with [ color = red ] 
;  [if any? other turtles-here with [sensed?] 
;  [set sensed? true
;    react ] ]
;end
;
;to react
;  ifelse sensed? [ ask target [ glow ] [ die ] [ fd 1 ] ]
;end

;;; the core procedure!
;to communicatett  ;; turtle procedure
;  if any? other turtles-here with [message?]
;    [ set message? true ]
;end
;
;; color turtles with message red, and those without message blue
;to recolor  ;; turtle procedure
;  ifelse message?
;    [ set color red ]
;    [ set color blue ]
;end
;
;to catch-sheep  ;; wolf procedure
;  let prey one-of sheep-here                    ;; grab a random sheep
;  if prey != nobody                             ;; did we get one?  if so,
;    [ ask prey [ die ]                          ;; kill it
;      set energy energy + wolf-gain-from-food ] ;; get energy from eating
;end


;;;
;;; plotting procedures
;;;

;; this draws a line at the given x-coordinate

to draw-vertical-line [x-val]
  set-plot-pen-color red
  plot-pen-up
  plotxy x-val 0
  plot-pen-down
  plotxy x-val number-nuclei
end 

;; this draws a line at the given y-coordinate

to draw-horizontal-line [y-val]
  set-plot-pen-color green
  plot-pen-up
  plotxy 0 y-val
  plot-pen-down
  plotxy ticks y-val
end 


; Copyright 1997 Uri Wilensky.
; See Info tab for full copyright and license.

There is only one version of this model, created over 7 years ago by Stina Krist.

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