CP15 – Gamma Absorption | Edexcel A Level Physics

Theory — Gamma Radiation Absorption

Gamma radiation is attenuated exponentially as it passes through matter.

What is Gamma Radiation?

Gamma (γ) radiation — electromagnetic radiation emitted from the nucleus of an unstable atom during radioactive decay
Very high frequency (> 10¹⁹ Hz) and very short wavelength (< 10 pm) — part of the EM spectrum beyond X-rays
No charge, no mass — travels at the speed of light; not deflected by electric or magnetic fields
Most penetrating of the three types of ionising radiation; stopped by several cm of lead or metres of concrete

Exponential Attenuation

When gamma radiation passes through a material, the count rate N decreases exponentially with thickness x:

N = N₀ e^(−μx) Taking natural log: ln(N) = ln(N₀) − μx

N₀ = corrected count rate with no absorber (s⁻¹) · μ = linear attenuation coefficient (cm⁻¹ or m⁻¹) · x = thickness of absorber (cm or m)

A graph of ln(N) vs x gives a straight line with gradient = −μ and y-intercept = ln(N₀).

Half-Value Thickness x½

The half-value thickness x½ is the thickness of lead needed to halve the count rate:

x½ = ln(2) / μ = 0.693 / μ

For gamma radiation from cobalt-60 in lead: x½ ≈ 1.0–1.2 cm. For lower-energy gamma sources: x½ is smaller (more easily absorbed).

Background Radiation

Even without a radioactive source, the Geiger-Müller tube detects a low level of ionising radiation from natural sources — cosmic rays, ground radiation, building materials. This is called background radiation.

All count rate measurements must be corrected: corrected count rate = measured count rate − background count rate. Background is measured with the source removed or shielded, taking a long count (at least 5 minutes) to reduce statistical uncertainty.

Geiger-Müller Tube

The GM tube detects ionising radiation by the ionisation it causes in a gas-filled tube. Each ionising event causes a brief electrical pulse — these pulses are counted. The count rate (counts per second, or counts per minute) is proportional to the intensity of radiation reaching the tube.

Statistical uncertainty in count rate: for N counts in time t, the uncertainty in count rate = √N / t. Longer counting times reduce this uncertainty.

⚠ Safety — Radiation Hazard

This experiment involves radioactive materials. Read and follow all safety rules before beginning.

⚠ Radiation Safety Rules (Schools)

Gamma sources used in schools are weak sealed sources (typically cobalt-60 or caesium-137, typically 185 kBq). They are designed to be safe when handled correctly.

Mandatory rules:

▸ Sources must be stored in lead-lined containers when not in use. ▸ Never handle a source directly — always use long-handled tongs. ▸ Point the source away from the body at all times. ▸ Minimise time with the source out of its container. ▸ Keep maximum distance from the source when possible — intensity falls as 1/r². ▸ Only the teacher should remove sources from storage.

⚠ CLEAPSS Guidance (L93)

▸ Radioactive sources must be registered and stored securely. ▸ A Radiation Protection Supervisor (RPS) must be consulted before the practical. ▸ Students must not handle the source directly under any circumstances. ▸ A risk assessment specific to the source and activity must be completed and approved before work begins. ▸ Hands must be washed after the practical session.

Risk Assessment

Hazard	Risk	Control measure
Gamma radiation	Ionisation of tissue (low risk for school sources)	Tongs; distance; minimise time; lead shielding
Lead absorbers	Lead dust ingestion (toxic)	Do not damage absorbers; wash hands after
GM tube electronics	High voltage (~400V)	Do not open or modify tube; follow standard electrical safety

In This Simulation

This simulation uses virtual radiation. No real radioactive sources are involved. The simulation models the statistical nature of radioactive decay (Poisson statistics) and realistic count rates for a weak cobalt-60 source with lead absorbers.

The purpose is to allow you to understand the experimental method, practice the data analysis, and prepare for the real practical — where all school safety rules and CLEAPSS guidance must be followed.

Procedure

Measuring corrected count rate through increasing thicknesses of lead.

Equipment

Gamma source (e.g. Co-60 or Cs-137, sealed school source) · Long-handled tongs · Lead absorbers of known thickness (0, 0.5, 1, 2, 3, 4, 5, 6, 7 cm) · GM tube and counter/ratemeter · Ruler · Lead-lined storage box

1

Measure background count rate

With the source in its lead storage box (not in the experiment), count for at least 5 minutes. Calculate the background count rate B in counts per second (or per minute). Record B — this will be subtracted from all subsequent readings.

💡 Long background count (5+ minutes) reduces statistical uncertainty in B from √N/t. A 1-minute count could have ~5% uncertainty; 5 minutes reduces this to ~2%.

2

Set up the apparatus

Place the GM tube in its holder. Place the gamma source at a fixed distance from the GM tube window (e.g. 10 cm). This distance must stay constant for all readings — moving the source changes the count rate via the inverse square law, not absorption.

💡 The teacher places the source using tongs. Students should stand back during source placement. Never handle the source directly.

3

Record count rate with no absorber

Count for at least 3 minutes with no lead between source and tube. Record counts C and time t. Calculate count rate = C/t. Record as N_measured at x = 0.

💡 Longer counting times reduce statistical uncertainty. For count rate of ~100 s⁻¹, counting for 3 minutes gives √(18000) ≈ 134 counts uncertainty, or about 0.7% — acceptable.

4

Insert lead absorbers and record count rate

Place lead absorbers between source and GM tube. Record total thickness x (cm) and count rate for each. Use absorbers of 0.5, 1, 2, 3, 4, 5, 6, 7 cm. Count for at least 3 minutes at each thickness.

💡 At greater thicknesses the count rate falls — count for longer to get the same statistical accuracy. If N falls to 20 counts/min, count for 10 minutes to get √200 ≈ 14 counts uncertainty (7%).

5

Correct for background

For each reading: corrected count rate N = N_measured − B. Use corrected count rates in all analysis.

💡 If the measured count rate at thick absorbers approaches the background rate, the experiment has reached its limit — the signal is lost in the noise.

6

Plot ln(N) vs x

Calculate ln(N) for each corrected reading. Plot ln(N) (y-axis) against x (x-axis). Gradient = −μ. Calculate half-value thickness x½ = ln(2)/μ.

💡 Do not plot raw count rates — the exponential shape is hard to analyse. The ln graph gives a straight line whose gradient directly gives μ.

      ⚠ Simulation only — no real radiation. Step 1: measure background (source removed). Step 2: insert source and vary lead thickness. Record corrected count rate at each setting.
    

Lead Absorber Thickness

x 0.0 cm

0 cm7 cm

Thickness x0.0 cm

Expected N—

Source

Source in experiment

Count Timer

Count time 60 s

30 s10 min

Press Start Counting to begin

Latest Reading

—

counts s⁻¹ (measured)

Background B— (not yet measured)

Corrected N—

ln(N)—

Readings: 0/8 minimum

Results Data Table

Background B = — (measure background first) counts s⁻¹. Corrected N = measured − B.

#	x / cm	Count / counts	Time t / s	N_meas / s⁻¹	B / s⁻¹	N = N_meas − B / s⁻¹	ln(N)	√N/t uncertainty
No data yet.

Graph & Analysis

Attenuation coefficient μ

—cm⁻¹ — from |gradient|

Graph parameters

Gradient (= −μ)—

y-intercept (= ln N₀)—

N₀ from intercept—

R²—

Half-value thickness x½—

Expected μ (Co-60 in Pb)~0.65 cm⁻¹

Interpretation

Record ≥5 readings to see analysis.

N vs x

The exponential curve confirms N = N₀e^(−μx). The theoretical curve using μ from the ln graph is shown in green for comparison.

Half-value thickness

x½ = ln(2)/μ—

N₀/2—

Discussion Questions

Write your answers and reveal model answers when ready.

Q1

Explain why background radiation must be measured and subtracted from all count rate readings in this experiment.

Background radiation is ionising radiation that reaches the GM tube from natural sources (cosmic rays, ground and building materials, trace radioactive elements in the surroundings) even when no experimental source is present. If background is not subtracted, the measured count rate N_measured = N_gamma + B, where N_gamma is the contribution from the gamma source and B is the background. Using N_measured instead of the corrected N_gamma = N_measured − B would make the count rates appear too high at all thicknesses. More importantly, at large absorber thicknesses where N_gamma approaches zero, the graph would plateau at the background rate rather than continuing to decrease — making the curve non-exponential and giving an incorrect (too small) gradient and therefore an incorrect (too large) μ.

Q2

Explain why the graph of ln(N) vs x is a straight line, and state what the gradient and y-intercept represent physically.

The corrected count rate follows N = N₀e^(−μx). Taking the natural logarithm of both sides: ln(N) = ln(N₀) − μx. This is of the form y = c + mx where y = ln(N), x = the absorber thickness, c = ln(N₀) and m = −μ. Since N₀ and μ are both constants for a given source and absorber material, the graph is a straight line. The gradient equals −μ (the linear attenuation coefficient, cm⁻¹), which characterises how strongly the absorber attenuates the radiation. The y-intercept equals ln(N₀), where N₀ is the corrected count rate with no absorber (x = 0). From the y-intercept: N₀ = e^(y-intercept), which can be compared with the directly measured count rate at x = 0.

Q3

Why is it important to count for longer at greater lead thicknesses, and how does counting time affect the statistical uncertainty in count rate?

Radioactive decay is a random (Poisson) process. The uncertainty in the total count N is √N (the standard deviation of a Poisson distribution). The count rate is N/t, and the uncertainty in count rate is √N/t = √(N/t)/√t = √(count rate/t). A higher count rate gives lower relative uncertainty; a longer count time also reduces it. At large thicknesses, the count rate from the source is very low. If the count time is kept the same, fewer counts are recorded, and √N/N (the relative uncertainty) is larger. For example: at x = 0, N = 500 counts in 60s → relative uncertainty ≈ √500/500 = 4.5%. At x = 6cm, N = 20 counts in 60s → relative uncertainty ≈ √20/20 = 22%. Counting for 10 minutes at x = 6cm: N ≈ 200 counts → relative uncertainty ≈ 7% — much more acceptable.

Q4

The half-value thickness of gamma radiation from cobalt-60 in lead is approximately 1.0 cm. Calculate the thickness of lead needed to reduce the count rate to 1% of its original value.

From N = N₀e^(−μx): 0.01 = e^(−μx). Taking ln: −μx = ln(0.01) = −4.605. So μx = 4.605. The attenuation coefficient μ = ln(2)/x½ = 0.693/1.0 = 0.693 cm⁻¹. Thickness x = 4.605/0.693 = 6.65 cm ≈ 6.6 cm. Alternatively: since each x½ = 1.0 cm halves the count rate, the ratio N/N₀ after n half-value thicknesses is (1/2)ⁿ. For N/N₀ = 0.01: (1/2)ⁿ = 0.01 → n = log(0.01)/log(0.5) = −2/−0.301 = 6.64. So x = 6.64 × 1.0 = 6.6 cm.

Q5

Suggest two reasons why the measured value of μ might differ from the accepted value for cobalt-60 in lead.

1. Background subtraction error — if the background was measured at a different time or location than the experiment readings, or if the background varied during the experiment (due to cosmic ray fluctuations or other sources in the room), the subtracted background B will be incorrect. An overestimated B gives corrected count rates that are too low, causing the line to be steeper (larger μ). An underestimated B gives a line that plateaus at large x, making it appear shallower (smaller μ) and non-linear. 2. Scattering (Compton scatter) — some gamma photons that would otherwise miss the GM tube are scattered by the lead absorbers back towards the tube, adding to the count rate. This effect is more significant at low photon energies. Scattering makes the count rate appear higher than expected at each thickness, reducing the apparent gradient and giving a smaller (underestimated) μ than the true attenuation coefficient. Using narrow-beam geometry (small solid angle from source to detector) reduces this systematic error.