Answer :
Final Answer:
The dose rate averaged over the whole body from swallowing 1.85 µCi of [tex]\(^{57}\)[/tex]Co is approximately 0.043 Gy/day.
Explanation:
To calculate the dose rate, first, we need to find the activity of [tex]\(^{57}\)[/tex]Co in becquerels (Bq). We convert the given activity from microcuries (µCi) to becquerels using the conversion factor [tex]1 µCi = \(3.7 \times 10^4\)[/tex] Bq. Then, we use the dose conversion factor for [tex]\(^{57}\)Co[/tex], which is 5.2 × 10⁻¹¹ Gy/Bq-s for an internal dose. Since we want to find the dose rate per day, we multiply by the number of seconds in a day. Dividing the result by the person's mass gives us the dose rate averaged over the whole body in grays per day (Gy/day).
The calculation is as follows:
[tex]Activity of \(^{57}\)Co = \(1.85 \, \mu Ci \times 3.7 \times 10^4 \, Bq/\mu Ci\) = \(6.845 \times 10^4 \, Bq\)[/tex]
[tex]Dose rate = \(\frac{{Activity \times Dose \, conversion \, factor \times 86,400 \, s/day}}{{70 \, kg}}\)[/tex]
[tex]\(= \frac{{6.845 \times 10^4 \, Bq \times 5.2 \times 10^{-11} \, Gy/Bq-s \times 86,400 \, s/day}}{{70 \, kg}}\)[/tex]
[tex]\(= 0.043 \, Gy/day\)[/tex]
Therefore, the dose rate averaged over the whole body is approximately 0.043 Gy/day.
