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Chapter 19: Problem 39

Technetium- 99 has been used as a radiographic agent in bone scans $(43 \mathrm{Tc} \text { is absorbed by bones). If } 43 \mathrm{Tc} \text { has a half-life of }\( 6.0 hours, what fraction of an administered dose of \)100 . \mu \mathrm{g}\( 43 \)\mathrm{Tc}$ remains in a patient's body after 2.0 days?

Short Answer

Expert verified
After converting 2 days to hours, we get 48 hours. Then, we calculate the number of half-lives by dividing the total time (48 hours) by the half-life period (6 hours), giving us 8 half-lives. To find the remaining fraction of Technetium-99, we use the formula \((\frac{1}{2})^n\), where n is the number of half-lives. In this case, the remaining fraction is \((\frac{1}{2})^8 = \frac{1}{256}\). Finally, to find the remaining dose, we multiply the initial dose (100 µg) by the remaining fraction: \(100 \times \frac{1}{256} = \frac{100}{256} \approx 0.391\, \mu g\). So, approximately 0.391 µg of Technetium-99 remains in the patient's body after 2 days.

Step by step solution

01

Convert days to hours

We need to convert the given days to hours since the half-life is in hours. 1 day = 24 hours 2 days = 2 × 24 hours
02

Calculate the number of half-lives

Determine the number of half-lives that have passed in 2.0 days (48 hours). Number of half-lives = total time / half-life period \(n = \frac{t}{T_{1/2}}\) Where: n = number of half-lives t = total time = 48 hours \(T_{1/2}\) = half-life period = 6 hours
03

Find the remaining fraction of Technetium-99

We use the formula: Remaining fraction = \((\frac{1}{2})^n\) Where n is the number of half-lives calculated in step 2.
04

Calculate the final answer

Substitute the values obtained in steps 2 and 3 into the formula to find the remaining fraction of Technetium-99. Then multiply this fraction by the initial administered dose (100 µg) to calculate the final fraction remaining in a patient's body.

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Most popular questions from this chapter

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