How long does it take for Tc-99m to reach a nearby hospital for a bone scan?

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The discussion focuses on calculating the activity of Tc-99m and determining the maximum transport time for a bone scan. The half-life of Tc-99m is 6.01 hours, and the initial calculations for decay constant and activity were incorrect. A revised decay constant was derived using the formula λ = ln(2) / T(1/2), leading to a more accurate value. The correct calculations are crucial for ensuring that the hospital receives sufficient activity for the procedure. Accurate measurement and understanding of decay constants are essential for effective radiopharmaceutical transport.
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The question is: The activity of a source of Tc-99m (half-life = 6.01 hours) is counted in an ionization
chamber in a radiopharmacy.

(b) 44989345 counts are counted in 5.0 seconds. What is the activity of this
sample and what is the error on this measurement?

(c) A nearby hospital carries out a procedure which requires 6.0 MBq of Tc-99m
radiolabelled to a phosphate analogue in order to perform a bone scan. What
is the maximum amount of time that can be taken to transport the sample so
that enough activity reaches the hospital?


I did b but I'm not sure how to do this question but this is how I answered it, i got the 9 from part b:

N= No x e^(-λt)
6 = 9 x e ^ ( - 0.0013 x t)
ln (2/3) = -0.0013 x t
t = 311.9 s
 
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melissaaa said:
The question is: The activity of a source of Tc-99m (half-life = 6.01 hours) is counted in an ionization
chamber in a radiopharmacy.

(b) 44989345 counts are counted in 5.0 seconds. What is the activity of this
sample and what is the error on this measurement?

(c) A nearby hospital carries out a procedure which requires 6.0 MBq of Tc-99m
radiolabelled to a phosphate analogue in order to perform a bone scan. What
is the maximum amount of time that can be taken to transport the sample so
that enough activity reaches the hospital?


I did b but I'm not sure how to do this question but this is how I answered it, i got the 9 from part b:

N= No x e^(-λt)
6 = 9 x e ^ ( - 0.0013 x t)
ln (2/3) = -0.0013 x t
t = 311.9 s

Hi melissaaa, Welcome to Physics Forums.

Please use the posting template provided to format your questions when you post the the Homework sections of PF.

You haven't explained the "-0.0013" value that you've used for the decay constant. Where did that come from? (Hint: it's related to the half-life, so check your calculation...)
 
I did it again and I think I got the decay constant wrong, is it meant to be:

T(1/2)= ln(2)/λ

λ= ln(2) /6.01 x 60 x 60
= 0.0000320367...
 
melissaaa said:
I did it again and I think I got the decay constant wrong, is it meant to be:

T(1/2)= ln(2)/λ

λ= ln(2) /6.01 x 60 x 60
= 0.0000320367...

Okay, that looks better. What units are associated with λ? Always provide units when you show results.

This new value for λ should lead you to a more reasonable result for part (c)...
 
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