A gamma-ray spectrometer records counts in a interval while characterising the…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Counting experiments: Poisson statistics and the root-n rule

Problem

A gamma-ray spectrometer records

n = 4

counts in a

600\,\mathrm{s}

interval while characterising the background inside a shielded enclosure. A laboratory report states: "the count is

4 \pm 2

, since

u(n) = \sqrt{4} = 2

." The tabulated

68\,\%

confidence interval for small counts gives, for

n = 4

, a true mean lying between

2.09

and

7.16

counts. ((a)) Explain why the root-

n

interval

4 \pm 2

(that is,

2

6

) is not an adequate description of the uncertainty here. ((b)) State the correct

68\,\%

interval for the count and convert it to an interval for the background rate.

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