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

[melissaaa]

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

 

[gneill]

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...)

 

[melissaaa]

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...

 

[gneill]

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)...