This question might be difficult for people who never encountered rare-event counting statistics before. You might learn in the lab of finding lifetime of radioactive materials that the error of counts is equal to the square roots of the number of counts. You might wonder why.
Actually, what you measure (i.e. count) is the mean of a random variable governed by rare-event statistics called Poisson distribution. The error, hence can be determined by the standard deviation, or square-root of variance from Poisson distribution. It turns out that the standard deviation is exactly square root of the mean. If you want to know why, check out Wikipedia.
Now, in order to establish the rate to an uncertainty of 1 percent, we need
So, we need
counts.
Now, from 10 seconds measurement, we have
counts.
Therefore, the student should wait for
to reach the 1 percent uncertainty.
The correct answer is (D). Only 14 of 100 people answered this question correctly.
ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน
