When a gamma photon interacts with the scintillation crystal of a gamma camera, the detector is temporarily unable to record subsequent events for a brief interval τ\tauτ, known as the dead time.
The relationship between the observed count rate R1 R_1\,R1 and the actual incident count rate R2 R_2\,R2 is given by:
τ=R2−R1R1×R2 \tau = \frac{R_2 - R_1}{R_1 \times R_2} τ=R1×R2R2−R1A gamma camera is positioned near a phantom source containing Technetium-99m. The distance is adjusted such that the observed count rate R1 R_1\,R1 is 480 s-1. Under these conditions, an average of 12 of the gamma photons incident on the crystal every second are not recorded due to dead time.
Calculate the dead time τ \tau\,τ for this detector. Give your answer to an appropriate number of significant figures and state the unit.
A medical physicist claims that if exactly 80 gamma photons are incident on the detector during a one-second interval, and the detector has a dead time of τ=0.005 s\tau = 0.005\text{ s}τ=0.005 s, then 100% detection efficiency is guaranteed because the cumulative dead time (80×0.005 s=0.4 s80 \times 0.005\text{ s} = 0.4\text{ s}80×0.005 s=0.4 s) is less than one second.
Explain, with reference to the nature of radioactive decay, why this claim is incorrect.
