During a bone scintigraphy scan using a gamma camera, a scintillation detector is placed over a patient's femur. When a gamma-ray photon is detected, the system cannot detect another photon for a duration tdt_dtd known as the dead time.
The relationship between the measured count rate R1R_1R1 and the actual count rate R2R_2R2 corrected for dead time is given by:
td=R2−R1R1×R2 t_d = \frac{R_2 - R_1}{R_1 \times R_2} td=R1×R2R2−R1The gamma camera is adjusted such that the measured count rate R1R_1R1 is 400 s−1400\text{ s}^{-1}400 s−1. On average, eight of the gamma photons that reach the detector each second are not recorded. Calculate the dead time tdt_dtd for this detector. Give your answer to an appropriate number of significant figures.
A clinician suggests that if exactly 505050 gamma photons enter the detector in one second and the dead time is td=0.005 st_d = 0.005\text{ s}td=0.005 s, all the photons must be detected because the total cumulative dead time is much less than one second. Explain, with reference to the nature of radioactive decay, why this suggestion is incorrect.
