Sealed Source Dose Budget for a School Survey
A high-school science club plans 10 weekly 2-hour surveys using a sealed Cs-137 check source (662 keV gamma) stored in a lab cabinet. Today the survey meter reads 20 µSv/h at 0.50 m from the unshielded source and 0.10 µSv/h background in the room. The club's dose constraint is 0.30 mSv per student for the 20-hour project. A 3 mm lead sheet is available; at 662 keV its attenuation factor is about 0.73. The storage cabinet is 1.5 m from the nearest desk. Students propose keeping the source at 0.50 m, adding the lead sheet, and working 2 h per week. The teacher must decide whether to approve that plan, move the source farther away, or do both. The meter's reading uncertainty is ±20%, and the club wants a defensible margin below its constraint, not a calculation that only just passes.
1. Calculate the 20-hour dose at 0.50 m with the lead sheet. Does the proposal meet the constraint with a defensible margin? Show the effect of the ±20% meter uncertainty.
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Unshielded, the dose rate is 20 µSv/h, so over 20 h the dose is 20 × 20 = 400 µSv = 0.400 mSv. The 3 mm lead sheet gives a factor of 0.73: 20 × 0.73 = 14.6 µSv/h, and 14.6 × 20 = 292 µSv = 0.292 mSv. The nominal margin below 0.30 mSv is only 0.008 mSv, about 2.7%. The meter uncertainty is ±20%, so a reading 20% high gives 0.292 × 1.20 = 0.350 mSv, which exceeds the constraint. Even before considering background, the plan is not defensible as the only control. A useful check is that the background adds only about 0.10 × 20 = 2 µSv, so it does not rescue the calculation. Reject the proposal as written: it relies on a thin lead sheet and a measurement that could easily be higher than the nominal value.
2. Compare moving the source to 1.5 m (no lead) with the proposed 0.50 m plus lead. Which control should the teacher choose, and what additional practical steps make the choice robust?
Read the worked answer
Inverse-square scaling gives the dose rate at 1.5 m: 20 × (0.50/1.5)² = 20/9 = 2.22 µSv/h. Over 20 h this is 44.4 µSv = 0.044 mSv, or about 0.046 mSv including background. Even a 20% high reading is only about 0.053 mSv, far below 0.30 mSv. By contrast, 3 mm of lead reduces the rate only to 73% of its unshielded value; reducing 20 µSv/h to 2.22 µSv/h would require a factor of about 0.11, roughly three half-value layers of lead at this energy, not one thin sheet. The teacher should choose distance first: store and use the source at 1.5 m or farther, in a locked cabinet, with tongs and no hand-held exposure. Add a controlled-area sign, a pre-use and post-use survey, dose badges, and a rule that only trained students approach the source. If a close geometry is essential, combine distance with shielding and a strict time limit, but do not rely on the 3 mm sheet alone.