An environmental physicist measures the activity of radon daughters collected on an…

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

An environmental physicist measures the activity of radon daughters collected on an air filter with a scintillation counter. With the loaded filter in the counter the gross rate (filter plus the room's own background) is

R_{\rm s} = 8.0\,\mathrm{s^{-1}}

; with a blank, unexposed filter in its place the background rate is

R_{\rm b} = 1.5\,\mathrm{s^{-1}}

. Both rates come from earlier runs long enough that their own uncertainty can be ignored when planning a new measurement. The net rate is wanted to a relative uncertainty of

2.0\,\%

, using the source and background counting times

t_{\rm s}

and

t_{\rm b}

that minimise

u(R_{\rm net})

for a given total time

T = t_{\rm s}+t_{\rm b}

. ((a)) Find the total counting time

T

needed to reach

2.0\,\%

relative uncertainty on the net rate, using the optimal division of time. ((b)) Find

t_{\rm s}

and

t_{\rm b}

for that total time.

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