Half life Tc-99m injected into a patient

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Homework Help Overview

The discussion revolves around the radioactive decay of Tc-99m, specifically focusing on calculating the remaining fraction of technetium in a patient after a specified time period. The half-life of Tc-99m is given as 6.03 hours, and the problem involves understanding the implications of this decay over a 36-hour period.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formula for radioactive decay and question the values used in calculations. There is a focus on the significance of the original amount of technetium injected and how it relates to the fraction remaining after decay. Some participants express confusion regarding the application of values from previous problems involving half-lives.

Discussion Status

The discussion is active, with participants questioning the assumptions made about the original amount of Tc-99m and its relevance to the calculations. There is a mix of interpretations regarding the setup of the problem, and some guidance has been offered about the correct approach to determining the fraction remaining.

Contextual Notes

Participants are navigating potential misunderstandings about the use of specific values in the decay formula and the implications of the half-life in relation to the original amount injected. There is a noted lack of consensus on how to interpret the problem correctly.

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Homework Statement



A patient comes into the hospital for a bone scan and is injected with a dye containing Tc-99m. The half-life of Tc-99m is 6.03 h. What fraction of the original technetium will remain the patient 36 h after the procedure if radioactive decay is the only means by which it is removed?

Homework Equations



The Attempt at a Solution



Af = Ao (1/2)t/h
Af = 99 (1/2)36/6.03
Af = 1.579214746

1.57921476 / 98 = 0.016

0.016 x 100 = 1.6 %

I am getting 1.6 % but the answer key states the answer as 0.016 %. What am I doing wrong. Is the m after Tc-99m play a role in this that I'm missing?
 
Last edited:
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No. Assume the original amount of TC-99 which is injected is 1.
 
But if its a ratio why does it matter what value I put in for the original amount? For example, for every other question involving half life I have used the amu given, i.e. Aluminium-30 I used 30 amu as the original and it always gives the right answer. So what is so unique about this question?
 
"What fraction of the original technetium will remain ... after 36 hours ..." So if the original amount of the sample is 100% of the total amount injected, then what fraction will remain after 36 hours have elapsed?
 
needingtoknow said:
Af = Ao (1/2)t/h
Af = 99 (1/2)36/6.03
Why are you substituting 99 there? That's not the amount of radioactive material. You want Af/Ao, right?
 

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