Physics IA · E · Nuclear and quantum physics · topic 28 of 30
Dice decay: does chance follow the exponential law? · IB Physics IA idea: guide, sample graph and step-by-step plan
simple kit. big ideas.Nobody can tell which die will 'decay' next. So why does the whole tray follow a smooth curve?
- ✓ you like simple kit and clear maths
- ✓ you can use a spreadsheet
- ✓ you want to see randomness turn into a law
The big idea
← p is not λ!Each atom has the same chance of decaying in a given time, and you cannot say when. Dice give you the same thing: each die has a fixed chance, p, of being removed each round. The number left should follow N = N₀(1 − p)ⁿ, an exponential. Chance per round is not the decay constant: link them with λ = −ln(1 − p). With few dice the curve is noisy; with many it is smooth. How many dice do you need? is the real question, and it makes a strong IA.
Make it yours: pick one twist
Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.
Swipe for more twists →
Remove only a six (p = 1/6), then also try 12-sided dice or coins (p = 1/2).
→ You compare several decay constants and half-lives, each predicted from p.Repeat with 10, 30 and 100 dice, several times each.
→ You measure how the scatter changes with N₀: a clean, quantitative question about statistics.Check how well a straight-line fit of ln N recovers λ when there are few dice.
→ Your evaluation becomes the study: how reliable is the fit?Simulate the dice in a spreadsheet with random numbers and compare with the real dice.
→ You can run thousands of atoms, and you must discuss how far a computer model is like a real one.Dice that 'decay' into a second kind of die that can also decay.
→ Goes beyond a single exponential: a daughter product that rises and then falls.Radiocarbon dating, or medical tracers with a short half-life.
→ Gives your introduction a purpose; the model and the graph stay the same.Your Physics IA research question: run the check
write it FIRST, then check itWrite your own question first. Then make sure it ticks every box:
- Names the independent variable (starting number of dice, or the chance per round) and its range.
- Names the dependent variable and how it is recorded (dice left, or dice removed per round, after each round).
- Says what stays the same: the dice, the tray, the rule for removal and the way of throwing.
- Says what you compare your data with (the exponential prediction from p) and how you will quantify the match.
- Is narrow enough for about 10 hours, with repeats at each setting.
The set-up
One way to run it. Draw your own version, with your real dice and your own table.
How your Physics IA could be laid out
The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.
Your question; why decay is random but follows a law; what you expect.
The exponential law; chance per round versus decay constant (λ = −ln(1 − p)); half-life in rounds; why scatter shrinks with more atoms; limits of a dice model.
Independent, dependent and controlled variables, with how each is set or kept the same.
Dice, tray, rule for removal, how you throw, how many rounds, how many repeats; enough detail to repeat it.
Short and specific: dice on the floor, noise, nothing hazardous. Keep this short.
One table per setting: round number, repeated counts and averages, with headers that carry units or 'number'.
Number left (or removed) per round, with repeats; averages and their spread.
A graph with the predicted curve, and a straight-line graph of ln N; the decay constant from the gradient, compared with the one predicted by p.
Answer with numbers: does the data fit the exponential, how close is λ to its prediction, and how many dice make the fit good?
Weaknesses ranked by their effect on your result, each with a specific, realistic improvement.
Every source for theory, method, data or simulation.
What your Physics IA graph could look like
Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only
- Axis labels name the quantity and show where the uncertainty comes from: here it is the spread of repeats, not a ruler.
- Error bars come from the spread of repeated runs, not a guess. Say how many repeats you used.
- The prediction is drawn from the chance p, not fitted to the data: that is what makes it a test.
- The y-axis starts at zero so the shape is honest.
- Another graph to consider: plot ln N against n. A straight line means exponential, and its gradient should be ln(1 − p), which you can compare with theory.
How many dice do you need?
how many dice? that's your RQTheory, not data: for p = 1/6 the relative scatter in the number removed in round one is about √(5/N₀). Compare it with your own repeats to see where chance stops hiding the law.
Your game plan
trial a full round first!Tick steps off as you go. We'll remember on this device.
0 of 11 done
- Read and predictFind the exponential decay law, the meaning of the decay constant and half-life. Work out what you expect for your chosen p before you throw a die.
- Trial run (1 lesson)Run one full round with a small tray. Is the rule clear (what counts as decayed)? Is the throw random? How long does a whole run take?
- Decide the settingsChoose the starting numbers or chances, how many rounds (until how few are left?) and how many repeats.
- Build your tableMake the table before you collect any data, with a column for every repeat.
- Collect the dataRecord the number left after each round. Keep the throw the same. Note any slip as it happens.
- ProcessAverage repeats, find the spread, and for each setting calculate the predicted curve from p.
- Graph and fitPlot data with the prediction, then ln N against round number and find the gradient. Compare it with the predicted λ.
- CompareDoes the data fit within the scatter you measured? How does the match depend on N₀?
- EvaluateRank what limited your result by its effect and make improvements specific.
- Write, then cutWrite in the order of the layout above and keep within 3,000 words: tables, graphs, equations and references are not counted, so let them carry detail.
- Check before your teacher's draftRun the checklist below, then get your RQ or draft checked. Your teacher reads one draft only, so make it count.
Physics you'll need
Traps to avoid in this Physics IA
- Too few dice: the data is so noisy you cannot tell an exponential from anything else.
- Mixing up chance per round and the decay constant: they are not the same number.
- Only one run per setting, so you do not know the scatter.
- Changing the rule between rounds, like re-throwing a die that landed on its edge.
- Counting dice 'left' at the start of a round in some runs and at the end in others.
- Saying a real nucleus is 'just like a die' without discussing what a dice model leaves out.
More Physics IA ideas like this
- Counting radiation: does it follow an inverse square?●●●
- Shielding radiation: the absorption coefficient●●●
- LED colours: can you measure Planck's constant?●●○
This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.