Physics IA · E · Nuclear and quantum physics · topic 29 of 30

Counting radiation: does it follow an inverse square? · IB Physics IA idea: guide, sample graph and step-by-step plan

safety first, and I mean it!

Light and gravity follow an inverse-square law. Does the radiation from a source do the same, or does something sneaky get in the way?

Difficulty●●● Stretch
KitAdvanced: teacher-supervised Geiger counter, or a simulation or published dataset
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like testing a law that sounds too neat
  • ✓ you can handle counting statistics
  • ✓ you are happy to use a simulation or dataset if needed

The big idea

← where is distance zero?

A small source sends radiation out in all directions, so the count rate should fall as 1/d². But your tube has its window inside its case, the radiation is random, and a beta source is partly absorbed by air. Your job: take the background out, test the inverse-square model, and find the real zero of distance. Because decay is random, every count has an uncertainty you can calculate. A strong IA says what the data does and does not support. Only a teacher or technician handles the source.

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 →

Find the true distance

Fit count rate against (d + d₀), where d₀ is the offset from the case to the source and the tube window, and treat d₀ as something to find.

→ Your graph has an extra unknown, and your analysis becomes a fit, not just a plot. Strong, because the offset is real.
Compare two kinds of radiation

If your teacher has them, compare a gamma-emitting source with a beta source, or use a dataset that has both.

→ Shows why air absorption bends the beta result but hardly touches the gamma one.
Count for longer

Repeat the series with counting times chosen so each count has about the same percentage uncertainty.

→ Your error bars become a design choice rather than a surprise.
Use a simulation or dataset

Use a radiation simulation or a published dataset, and treat it as a model, not as your experiment.

→ No source in the room. The IA is about analysing the data and evaluating the model's assumptions, and you must state clearly where the data came from.
Test the exponent

Fit count rate against d with a power law and ask what exponent you get, with an uncertainty.

→ You are asking 'is it 2?' instead of assuming 2.
Change the context

Relate it to a safe working distance from a source, such as how far back to stand.

→ Gives your introduction a purpose; the physics and the graph stay the same.

Your Physics IA research question: run the check

say which route you use

Write your own question first. Then make sure it ticks every box:

  • Names the independent variable (distance, from where to where, how many values) and the dependent variable (count rate, from what counting time).
  • Says how background is measured and subtracted, and for how long.
  • Says exactly what distance means: from which part of the source to which part of the tube.
  • Says what model you test (1/d² with an offset, or a power-law exponent).
  • Makes the route clear: school-supervised experiment, or a named simulation or dataset, and why it is realistic.

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The set-up

One possible arrangement, for a teacher-supervised experiment. If you use a simulation or dataset, draw the set-up that produced it.

dsealed source in its holder:teacher handles itmeasure d to the windowtube slides on a ruler railcounter: fixed time

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.

Research question and context~250
Your question; where radiation falling with distance matters (safety, detectors, medical imaging); what you expect and why.
Background physics~450
The inverse-square model and why a point source gives it; random decay and √N uncertainty; background; the assumptions that could fail (offset, air, dead time).
Variablestable
Independent, dependent and controlled variables, with how each is set or kept constant; for a dataset, which variables the original author controlled.
Method~400
Apparatus with resolutions, or the source of your data and why it is suitable; how background is taken; how distance is defined; counting times and repeats.
Safety, ethics, environment~80
Specific rules: the source is handled only by the teacher or technician, kept in its container, and your school's radiation rules are followed. If you did not use a source, say so.
Raw datatable
One table: distance, counts, time, and a separate background table, with units and uncertainties.
Processing~250
Background-corrected rates with uncertainties from the number of counts; one worked example of each calculation type.
Graphs and analysis~350
A graph that tests the model (not just plots it), error bars, and what the fit says about the exponent or the offset.
Conclusion~400
Answer with numbers: does the data support 1/d² within uncertainty, over what range, and what would explain departures?
Evaluation~650, the biggest part!
Weaknesses ranked by their effect on your result, each with a specific, realistic improvement.
Referencesnot counted
Every source for theory, method, data or simulation.

What your Physics IA graph could look like

√N error bars ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

0246810121416180100020003000400050006000Distance d from the case / cm (± 0.1 cm)Corrected count rate R / counts per min (± √N)inverse square with an offset d₀inverse square from the caseyour data, with error barsthe dashed curve assumes d is measuredto the right place. Is it?ILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity, the unit and the uncertainty. Background is already subtracted, and the text says so.
  • Counting uncertainty is √N, so the bars are longer where counts are higher but relatively longest at large distances.
  • Two versions of the model drawn, so you can see how much the offset matters at small d.
  • The two models almost agree far away and disagree most close up: that is where your data is most informative.
  • Another graph to consider: plot R against 1/(d + d₀)². If the model holds, that is a straight line through the origin, and you can change d₀ to find the best straight line.

Which uncertainty matters most?

Rank by the effect on your result: the corrected count rate at one distance (here d = 8 cm). Counting statistics and the unknown offset are different kinds of problem, and the chart makes you say which one to attack first.

Unknown zero of distance (± 0.5 cm)10.5%Counting statistics (1 min)5%Reading the ruler (± 1 mm)2.1%Background count (10 min)0.4%biggest effect: discuss this first!% uncertainty in R at d = 8 cmILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

agree the safety route first

Tick steps off as you go. We'll remember on this device.

0 of 11 done

  1. Read and predictFind the inverse-square law and the idea of random decay. Predict the graph of count rate against distance, and say which assumptions could make it differ.
  2. Settle the route and the safetyAgree with your teacher: supervised experiment, simulation or published dataset. A source is handled only by the teacher or technician, and school radiation rules are followed. If the answer is no source, that is a fine IA.
  3. Trial run (1 lesson)Count background for a few minutes. Try a few distances. Is the source aligned with the tube? Are the counts large enough at the largest distance?
  4. Decide range, times and repeatsChoose at least 6 distances and choose counting times so the uncertainty is similar at each. Write down why.
  5. Define distance exactlyDecide where distance is measured from and to, and how you will check for an offset.
  6. Collect the dataTake background before and after. Record the number of counts and the time, not only the rate.
  7. ProcessSubtract background, calculate rates and the uncertainty from the counts, and carry them through.
  8. Graph and fitChoose a graph that tests the inverse-square model with a straight line if you can. Decide what the gradient or intercept would mean.
  9. EvaluateRank the sources of uncertainty by their effect on your answer and make each improvement specific.
  10. 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.
  11. 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

  • Handling a source yourself or ignoring school rules: the source is for the teacher or technician only.
  • Forgetting background, or measuring it for too short a time.
  • Measuring d from the outside of the case when the detecting window is inside it.
  • Counting too few events: with only 100 counts, the uncertainty is already 10%.
  • Assuming inverse-square for a beta source in air without checking absorption.
  • Treating simulation or dataset output as your own measurement without saying where it came from.

More Physics IA ideas like this

Make sure it's yours

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.

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