A gamma source is placed 0.20 m from a Geiger–Müller tube. The measured count rate is 480 counts per minute. The background count rate is 30 counts per minute.
(a) Calculate the count rate you would expect to measure when the tube is 0.50 m from the source. Assume no absorption of gamma radiation in the air. [3]
(b) Suggest why the distance from the source to the tube may be subject to a systematic error. [1]
- (a) corrected count rate at 0.20 m = 480 − 30 = 450 counts min$^{-1}$(1)
- (a) inverse square law: $450 \times \left(\frac{0.20}{0.50}\right)^2$ = 72 counts min$^{-1}$(1)
- (a) measured count rate = 72 + 30 = 102 counts min$^{-1}$ (allow 100)(1)
- (b) the position of the source inside its sealed holder/capsule is not known exactly, so the measured distance is not the true distance from the source (accept: radiation is detected at an unknown point inside the GM tube, not at its window; ruler zero/end not aligned with source or detector)(1)
- Answer: (a) 102 counts min$^{-1}$
- Examiner tip: Only the source's count rate obeys the inverse-square law — subtract background first, then add it back for a 'measured' value.