Gamma absorption by lead

Practical method

Aim

Investigate the absorption of gamma radiation by lead and determine the linear attenuation coefficient and half-value thickness.

Variables

Independent variable: thickness of lead x
Dependent variable: corrected count rate C
Control variables: source–detector distance; counting time; the same source.

Apparatus

• Sealed cobalt-60 source
• GM tube and counter
• Lead sheets of known thickness
• Micrometer
• Fixed holder for source and tube
• Tongs

Method

1. Measure the background count rate.
2. Fix the source and GM tube a set distance apart.
3. Measure the count rate with no lead, then with lead thicknesses up to 20 mm (measured with a micrometer).
4. Subtract background. I = I₀\(e^{-\mu x}\), so plot ln C against x: gradient −μ.
5. Half-value thickness x½ = \(\dfrac{\ln 2}{\mu }\).

Sample results

Background subtracted. Fixed source–tube distance.

Analysis

ln C falls linearly with x, gradient −0.060 mm⁻¹, so μ = 60 m⁻¹ and the half-value thickness is \(\dfrac{\ln 2}{60}\) = 0.0116 m = 11.6 mm. Every 11.6 mm of lead halves the count rate.

Uncertainty

Counting errors (√N) dominate; at the thickest lead, longer counts are needed. Lead thickness by micrometer is precise (±0.01 mm).

Errors and improvements

Risk assessment

Common mistakes

• Plotting C against x and reading a 'gradient'.
• Forgetting background.
• Changing the source–tube distance between readings.

Worked analysis

Gradient = \(\dfrac{3.586 - 4.787}{20}\) = −0.060 mm⁻¹, so μ = 0.060 mm⁻¹ = 60 m⁻¹. x½ = \(\dfrac{\ln 2}{0.060}\) = 11.6 mm.

Common misconception

No thickness of lead stops all gamma radiation; it reduces the intensity exponentially, halving for each half-value thickness.