Choosing Sources for a Foil Gauge and a Pipeline Tracer
A small industrial physics laboratory must set up two measurements using only sources already in its store. (i) Continuous gauging of the thickness of aluminium foil leaving a rolling mill at 0.05 mm, where the gauge must detect a 1 % thickness change and hold its calibration for years without re-standardising. (ii) Tracing the flow of brine through a 40 m buried steel pipeline, where a pulse of tracer is injected and counted by a scintillation detector at the far end, the transit taking about 30 hours. Available are Am-241 (5.5 MeV alpha, 59.5 keV gamma, half-life 432 y), Sr-90 in equilibrium with Y-90 (beta up to 2.28 MeV, half-life 28.8 y), I-131 (beta plus 364 keV gamma, half-life 8.0 d) and Na-24 (2.75 MeV gamma, half-life 15 h). A freshly prepared 400 MBq Na-24 source is ready at 08:00 on Monday, and the far-end counter needs at least 20 MBq at the moment of passage. Health physics demands the smallest reasonable dose and a sealed source wherever possible.
1. Choose the source for the foil gauge and justify the choice quantitatively, using ranges and attenuation. Explain why the other three are unsuitable.
Read the worked answer
Am-241 (alpha): rejected. A 5.5 MeV alpha has a range of only about 20–25 µm in aluminium - less than half of 50 µm - so no alpha emerges and there is no transmitted signal to measure.
Am-241 (59.5 keV gamma): rejected on sensitivity. For aluminium at 60 keV, μ/ρ ≈ 0.28 cm² g⁻¹, so μ ≈ 0.75 cm⁻¹. Over x = 0.005 cm, μx ≈ 3.8 × 10⁻³. A 1 % change in thickness changes μx by 3.8 × 10⁻⁵, so the transmitted count changes by only about 0.004 % - hopeless against counting statistics. Gamma rays simply pass through thin foil.
I-131 and Na-24: rejected on both counts - still too penetrating for 50 µm of aluminium, and their half-lives (8.0 d, 15 h) would force re-standardisation within days, violating the “years of stable calibration” requirement.
Sr-90/Y-90 chosen. The 2.28 MeV betas have a range of roughly 4 mm in aluminium, so 0.05 mm removes a modest but measurable fraction of them; the transmission curve is steep enough in this region to register a 1 % thickness change provided counting statistics are good (long counting times, strong source). The 28.8 y half-life gives the required year-to-year stability, and the source is used sealed behind a thin window. Beta gauges are the standard industrial choice for foil in this thickness range; a lower-energy beta emitter or a soft X-ray source such as Fe-55 would give still better sensitivity if it could be obtained.
2. Choose the tracer for the pipeline and compare the two gamma emitters on physics, chemistry and dose. Compute the activity margin for Na-24 over the 30-hour transit and the maximum tolerable delay.
Read the worked answer
Physics. Na-24 emits 2.75 MeV gamma, which penetrates 40 m of soil and a steel wall with modest attenuation. I-131's 364 keV gamma is attenuated far more by that much earth and steel, so the count rate at the far end would be poor.
Chemistry - the decisive point. The tracer must follow the brine, i.e. the chloride/water flow. Na-24 injected as sodium chloride solution is chemically identical to the brine and travels with it. Iodide is not: it sorbs on pipe walls and corrosion products, tails behind the flow and gives a smeared, delayed arrival curve.
Dose and aftermath. I-131 is a beta emitter with an 8-day half-life; it lingers, and any ingestion concentrates it in the thyroid. Na-24 decays by 0.4 % in five days (2⁻⁸), so the pipeline becomes usable again quickly and the total dose commitment is smaller.
Activity margin. After 30 h = 2 half-lives, A = 400/4 = 100 MBq, five times the 20 MBq threshold. Requirement: 400 × 2⁻ⁿ ≥ 20, so 2ⁿ ≤ 20, n ≤ 4.32, i.e. a maximum of 4.32 × 15 ≈ 65 h after preparation. Beyond that the pulse is undetectable and a fresh batch must be activated. If the pump fails, the run must start within about 65 h of 08:00 Monday.
3. The gauge source must be sealed while the tracer is deliberately released. Explain, in terms of the interaction of the radiations with matter, why the same isotope that is safe in a sealed capsule would be dangerous if released, and how this shapes the choice of source for each job.
Read the worked answer
External versus internal exposure. Alpha and beta particles lose energy very rapidly in matter: an alpha is stopped by a few centimetres of air, a sheet of paper, or the dead outer layer of skin; a beta by a few millimetres of aluminium or a few metres of air. Outside the body they deliver dose only to the surface, so a sealed alpha or beta source - exactly what the foil gauge needs - is safe to handle with ordinary precautions.
If released. Inside the body the same short range is a liability: all the energy is deposited in a small volume of living tissue. An alpha emitter lodged in the lung delivers a large local dose over a tiny mass, which is why Am-241 must never be an unsealed tracer. Sr-90 is a bone-seeking calcium analogue and its betas irradiate bone marrow - so it is used sealed, never injected.
Consequence for the choice. A gauge needs a penetrating radiation only as far as the foil, so it uses a sealed beta source with a thin window, checked for leakage. A flow tracer must be released into the environment, so it must be a gamma emitter (the radiation escapes the pipe to be detected), chemically matched to the flow, and short-lived so that it disappears. The rules therefore pull in opposite directions, and no single isotope satisfies both jobs - which is why two different sources are selected here.