A student makes 10 one-second measurement of the disintegration of a sample of a long lived radioactive isotope and obtains a following values:
3, 0, 2, 1, 2, 4, 0, 1, 2, 5.
How long should the student count to establish the rate to an uncertainty of 1 percent?
A. 80 s
B. 160 s
C. 2000 s
D. 5000 s
E. 6400 s
(GR0177 #16)
Solution:
Radioactive decay can be described by Poisson Distribution.
Poisson Distribution (PD):
Probability distribution of discrete events over an interval (time. distance, etc)
In PD, Standard Deviation, σ = √μ (see problem GR8677 #40)
μ = λT = expected value
λ = average rate
T = time interval
% Uncertainty = (σ/μ) × 100%
σ/μ = 0.01
√μ/μ = 10−2
μ/μ2 = 10−4
1/μ = 1/104
μ = λT = 104
λ = (3 + 0 + 2 + 1 + 2 + 4 + 0 + 1 + 2 + 5)/10 = 2
T = 104/2 = 5000
Answer: D
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