Calculate the percent efficiency of an uptake probe if a radioactive source of 21.9 nCi gives a count rate of 7,250 cpm with the probe.
Answer (1)
Convert the activity from nCi to dpm using the conversion factor 1 nCi = 2.22 dpm: A c t i v i t y d p m = 21.9 × 2.22 = 48.618 dpm.
Calculate the percent efficiency using the formula: E ff i c i e n cy = A c t i v i t y d p m C o u n t R a t e × 100 .
Plug in the given count rate of 7,250 cpm: E ff i c i e n cy = 48.618 7250 × 100 .
The percent efficiency of the uptake probe is approximately 14912.17% .
Explanation
Problem Analysis We are given a radioactive source with an activity of 21.9 nCi and a count rate of 7,250 cpm when measured with an uptake probe. Our goal is to calculate the percent efficiency of the probe.
Converting Units First, we need to convert the activity from nCi (nanoCuries) to dpm (disintegrations per minute). We know that 1 nCi is equal to 2.22 dpm.
Calculating Activity in dpm Now, we calculate the activity of the source in dpm: A c t i v i t y d p m = 21.9 n C i × 2.22 d p m / n C i = 48.618 d p m
Calculating Efficiency Next, we calculate the percent efficiency of the probe using the formula: E ff i c i e n cy = A c t i v i t y d p m C o u n t R a t e × 100 We are given the count rate as 7,250 cpm.
Final Calculation Now, we plug in the values into the formula: E ff i c i e n cy = 48.618 d p m 7250 c p m × 100 = 14912.172446419021 Therefore, the percent efficiency of the uptake probe is approximately 14912.17%.
Final Answer The percent efficiency of the uptake probe is approximately 14912.17%.
Examples
Understanding the efficiency of uptake probes is crucial in medical imaging and nuclear medicine. For instance, when diagnosing thyroid disorders using radioactive iodine, knowing the probe's efficiency helps doctors accurately measure the iodine uptake by the thyroid gland. This ensures precise diagnosis and appropriate treatment planning, highlighting the importance of efficiency calculations in healthcare.
