A weak radioactive source is counted on a detector that also registers a steady background
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement
Mathematical Methods for Physics, Ch Probability, random variables and distributions
Problem
A weak radioactive source is counted on a detector that also registers a steady background. With the source in place the detector records 2500 counts in 100s; with the source removed it records 900 counts in 100s. All counts arrive independently.
((a)) Find the net count rate due to the source and its standard deviation.
((b)) A repeat of the experiment may again use 200s of counting in total, split in any way between the two runs. Taking the two rates to be those just measured, find the split that makes the standard deviation of the net rate smallest, and that smallest value.