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

Shielding radiation: the absorption coefficient · IB Physics IA idea: guide, sample graph and step-by-step plan

a lovely straight-line experiment

How much lead stops half the radiation? The answer sits in one number, and you can measure it from a straight line.

Difficulty●●● Stretch
KitAdvanced: teacher-supervised Geiger counter and absorbers, or a dataset
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like linearising an exponential
  • ✓ you can work with counting uncertainty
  • ✓ you are happy to use published data if your school says no

The big idea

← subtract background FIRST

Each layer of absorber removes the same fraction of the radiation that reaches it, so count rate falls exponentially: R = R₀e^(−μx). Take the natural log and you get a straight line whose gradient is −μ. Subtract background first, or the line will curve. Then find the half-value thickness ln2/μ and ask how good your μ really is. For beta radiation the fall is not purely exponential, so choose and justify your radiation type. 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 →

Compare materials

Repeat with two materials, such as aluminium and lead, and compare their coefficients.

→ Your conclusion compares two numbers with uncertainties, and you can relate μ to density.
Use the mass attenuation coefficient

Divide μ by density and ask whether materials collapse onto a common value.

→ Adds a testable idea about what matters physically: how many atoms are in the way.
Use a dataset or simulation

Take published attenuation data or a simulation and analyse it exactly as you would your own.

→ No source. Your IA is analysis and evaluation of data you must cite and critique, saying what you do not know about how it was taken.
Test the exponential shape

Plot ln R against thickness and ask whether it is straight over the whole range, or bends at large thickness.

→ The model is tested, not assumed. Bends can point to scatter, background or an unsuitable source.
Check the half-value thickness

Find it directly from the graph, then compare it with ln2/μ from the gradient.

→ Two routes to the same quantity: their consistency becomes your evidence.
Change the context

Link it to shielding for X-ray rooms, medical staff or food irradiation.

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

Your Physics IA research question: run the check

state your route and radiation type

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

  • Names the independent variable (thickness, in which units, over what range) and the material.
  • Names the dependent variable (count rate, background-corrected, from what counting time).
  • Says what stays fixed: source, source-to-tube distance, counting time, geometry.
  • Says what you will find: the absorption coefficient, and from which graph.
  • Makes the route clear (supervised experiment, dataset or simulation) and why the radiation type suits an exponential model.

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The set-up

One possible arrangement for a teacher-supervised experiment. If you use a dataset, draw the set-up its authors used.

xsealed source: teacher handles itstack of sheets: add one at a timefewer get throughsource and tube: never move themcounter

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 shielding matters (medical, nuclear, safety); what you expect.
Background physics~450
Fractional absorption per layer and the exponential law; linearising with ln; half-value thickness; why background must be subtracted; limits of the model for your radiation type.
Variablestable
Independent, dependent and controlled variables, with how you set or keep them constant.
Method~400
Apparatus with resolutions, or the source of your data; how thickness is measured; how geometry is fixed; background; counting times and repeats.
Safety, ethics, environment~80
Specific rules: source handled only by the teacher or technician, and your school's radiation rules. Lead sheets are toxic: gloves, or wash your hands after. If you used data, say that no source was handled.
Raw datatable
One table: thickness, counts, time, plus a background table, with uncertainties.
Processing~250
Background-corrected rates and their uncertainties; ln R and its uncertainty; one worked example of each.
Graphs and analysis~350
Plot ln R against thickness, error bars, a line of best fit and what its gradient gives; test whether it is straight.
Conclusion~400
Answer with numbers: μ with uncertainty, half-value thickness, and how well an exponential describes your data.
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

error bars from √N ✓

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

024681012141618201.01.21.41.61.82.02.22.42.62.83.03.2Absorber thickness x / mm (± 0.5 mm)ln(R), R in counts per s (± 0.05)background-corrected: a straight linebackground (0.5 counts per s) left in: it bendsyour data, with error barsgradient = −μ. What are itsunits, and how big is its uncertainty?ILLUSTRATIVE · MADE-UP DATA
  • The y-axis is ln of a quantity with units. Say what units R had; the log itself has none.
  • Error bars: the uncertainty in ln R is about 1/√N, so points far through the absorber have bigger bars.
  • Both versions drawn to show what failing to subtract background does to the shape.
  • The gradient is −μ. Draw the steepest and shallowest lines through the error bars to get its uncertainty.
  • Another graph to consider: plot R (not ln R) against thickness and fit an exponential in your software, then compare the two values of μ.

Which uncertainty matters most?

Rank by the effect on your result, the absorption coefficient μ, not on the raw readings. Counting statistics usually win, but it is worth checking before you assume.

Counting statistics6.9%Uneven sheet thickness (± 0.5 mm)2.8%Source-tube spacing changes (1 mm in 100)1.9%Background subtraction1.8%Micrometer reading (± 0.05 mm)0.3%biggest effect: discuss this first!% uncertainty in μ, from the gradient between 0 and 18 mmILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

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

0 of 11 done

  1. Read and predictFind the attenuation law, the meaning of μ and the half-value thickness. Predict the graph shape and check whether your radiation type should be exponential.
  2. Settle the route and the safetyAgree with your teacher: supervised experiment, dataset or simulation. A source is handled only by the teacher or technician, following school rules.
  3. Trial run (1 lesson)Background first. Then a few thicknesses. Is the count high enough with the thickest absorber? Do the sheets stay in the same position?
  4. Plan thicknesses and timesChoose at least 6 thicknesses over a wide range and counting times that give similar relative uncertainty.
  5. Fix the geometryDecide how the source, the sheets and the tube are held so that nothing moves between measurements.
  6. Collect the dataRecord counts and times, not only rates. Measure thickness with a suitable instrument, in several places.
  7. ProcessSubtract background, find rates and ln R with uncertainties.
  8. Graph and fitPlot ln R against thickness, add error bars and best and worst lines, and get μ with an uncertainty.
  9. EvaluateRank sources of uncertainty by their effect on μ. Make every 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

safety is not optional
  • Source safety: only the teacher or technician handles a source, and school rules always apply.
  • Not subtracting background, so ln R curves at large thickness.
  • Moving the source or tube when adding sheets, so the geometry changes as well as the thickness.
  • Taking a thickness from the packaging instead of measuring it, or assuming sheets are uniform.
  • Using a beta source and forcing a straight line without saying why it might not be one.
  • Treating a dataset as your own measurement without citing it and discussing its limits.

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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