A nuclear-medicine physicist is checking the shielding around an iodine-131 dose…

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 nuclear-medicine physicist is checking the shielding around an iodine-131 dose calibrator with a Geiger counter. A preliminary run, long enough that its own uncertainty can be ignored for planning purposes, gives a gross count rate with the vial in place of

R_{\rm s} = 45.0\,\mathrm{s^{-1}}

and a background rate, measured with the vial removed, of

R_{\rm b} = 3.2\,\mathrm{s^{-1}}

. A follow-up session of total duration

T = 3600\,\mathrm{s}

(one hour) is available, to be divided between counting with the vial in place (

t_{\rm s}

) and counting the background alone (

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

), with the aim of making the net rate's uncertainty as small as possible. ((a)) Find the division of the hour,

t_{\rm s}

and

t_{\rm b}

, that minimises the uncertainty of the net rate. ((b)) Find

u(R_{\rm net})

for that division, and compare it with the uncertainty that an equal fifty-fifty split of the hour would have given, stating the percentage by which the equal split is worse.

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