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

In summary, we can use the formula N= No x e^(-λt) to determine the activity and error of a sample of Tc-99m in an ionization chamber, with a half-life of 6.01 hours. By plugging in the given values, we can find that the activity of the sample is 9 and the error on this measurement is 0. However, in part (c), we need to determine the maximum amount of time it takes for enough activity to reach a nearby hospital for a bone scan. To do this, we can use the decay constant (λ= 0.0000320367...) to find that the maximum time is approximately 259,596 seconds, or 72
  • #1
melissaaa
3
0
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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  • #2
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...)
 
  • #3
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...
 
  • #4
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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  • #5


Thank you for your question. I can provide a response to your inquiry about the time it takes for Tc-99m to reach a nearby hospital for a bone scan.

First, let's discuss the activity of a source of Tc-99m in a radiopharmacy. The half-life of Tc-99m is 6.01 hours, which means that after 6.01 hours, the activity of the sample will decrease by half. Using this information, we can calculate the activity of the sample in question.

To do this, we can use the equation A = A0 x (1/2)^(t/t1/2), where A is the current activity, A0 is the initial activity, t is the time elapsed, and t1/2 is the half-life.

Substituting the given values, we get A = A0 x (1/2)^(5.0/6.01) = A0 x (0.831) = 9 counts.

Therefore, the activity of the sample is 9 counts, and the error on this measurement can be calculated using the standard error formula, which is error = √N, where N is the number of counts. In this case, the error is √9 = 3 counts.

Moving on to part c, we are given that a nearby hospital requires 6.0 MBq of Tc-99m radiolabelled to a phosphate analogue for a bone scan. To determine the maximum amount of time it can take for the sample to reach the hospital, we need to calculate the amount of Tc-99m activity that will reach the hospital after the transport time.

To do this, we can use the same equation as before, but this time we are solving for t. Substituting the given values, we get t = t1/2 x ln (A/A0) = 6.01 x ln (6.0/9) = 4.02 hours.

Therefore, the maximum amount of time it can take for the sample to reach the hospital is 4.02 hours. This is assuming that the sample is transported immediately after the 5-second count, and there is no further decay during transport. Any additional time taken for transportation will result in a decrease in activity, which may affect the accuracy of the bone scan.

I hope this helps to answer your question. Please let me
 

1. What is radioactivity?

Radioactivity is the process by which unstable atomic nuclei emit radiation in the form of particles or waves. This process occurs naturally in some elements and can also be induced through nuclear reactions.

2. How does radioactivity affect living organisms?

Exposure to high levels of radioactivity can damage cells and DNA, leading to health problems such as cancer. However, low levels of radioactivity are present in our environment and can be found in some foods, and do not typically pose a significant health risk.

3. What are the different types of radiation emitted by radioactive materials?

The three main types of radiation are alpha particles, beta particles, and gamma rays. Alpha particles consist of two protons and two neutrons and have a low ability to penetrate matter. Beta particles are high-speed electrons and can penetrate deeper into matter. Gamma rays are high-energy photons and can penetrate the most matter.

4. How is radioactivity measured?

Radioactivity is measured using units such as becquerels (Bq) or curies (Ci), which represent the rate at which a material undergoes radioactive decay. Another common unit is the sievert (Sv), which measures the potential health risk from exposure to radiation.

5. What are some common sources of radioactivity?

Natural sources of radioactivity include radioactive elements found in rocks and soil, as well as cosmic rays from space. Artificial sources include nuclear power plants, nuclear weapons, and medical procedures such as X-rays and radiation therapy.

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