Question 1 Answer

The expected ratio of efficiency for PET isotopes relative to the efficiency for Cs-137:

Fraction of 662 keV photons attenuated by 2.54 cm NaI is 1 – e^{-(2,54 cm x 0.0775 cm2 g-1 x 3,67 g cm-3)} = 0.51 or 51%

Fraction of 511 keV photons attenuated by 2.54 cm NaI is 1 – e^{-(2.54 cm x 0.090 cm2 g-1 x 3.67 g cm-3)} = 0.57 or 57%

Ratio of expected efficiencies is (0.57 × 2)/(0.51 × 0.85) = 2.6

Question 2 Answer

Expected efficiencies for the Cs-137 source at each distance:

(See Establishing Detection Efficiency for Surface Contamination Measurements: Verification Calculations and Examples [HP Corner from February] for an example of calculating a geometry factor)

Question 3 Answer

Explanation:

10 µCi = 3.7 E10 Bq Ci^-1 x 1 E-5 = 370 kBq

370 kBq × 0.85 photons/decay = 314,500 photons sec^-1

Efficiency of detection for 662 keV gamma is 0.51

On contact, the expected count rate is 314,500 photons sec^-1 x 0.50 (geometry factor) x 0.51 = 80,179 CPS, but dead time is 10 µsec.

80,179 pulses per sec x 1E-5 sec per pulse = 0.82 or 82% dead time

This means that the detector is essentially OFF most of the time. Counts per Bq efficiency for Cs-137 on contact should thus be no more than 0.18 (live time) x 0.22 = 4%. But this does not account for the additional pulse “pile-up” effect, which will make the issue worse due to multiple interactions being counted as a single pulse. Assuming roughly 50% of interactions counted as 1 pulse will only get about 2%. (This is a guesstimate—you can do the experiment if you want the real numbers!)

At 1 cm, dead time is 314,500 photons sec^-1 x 0.19 geom x 0.51 × 1E-5 = 30%

Derived Cs-137 efficiency will thus be no more than 0.7 × 8.2% = 5.7%

At 2.5 cm, with a dead time of 8.7%, expect about 2.1% efficiency—this agrees with the measured value within the experimental uncertainty.

At 10 cm and 30 cm, dead time is ideal (<1%) and measured values agree with estimates within the experimental uncertainty, which would almost certainly be no better than ±25%.