Half-Life real life application question

In summary, to determine the volume of blood in a patient's body, a nuclear medicine technologist can use the formula A = Ao[(1/2)^(t/half life)], where A is the final activity, Ao is the initial activity, t is the time passed, and half life is the half life of the isotope. By plugging in the given values and solving for the final activity, we can then use the final activity in the same formula to solve for the volume of blood. In this case, the volume of blood in the patient's body is approximately 16336.36 cm^3.
  • #1
EIGHTSIX7
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Homework Statement



To determine volume of blood in a patient's body, a nuclear medicine technologist is injected a small amount of a radioactive isotope (T(1/2)= 45 min) into the patient's blood stream.

The activity of this isotope is at the time of injection was ( 2.8x10^4 decays/second ) If, after three hours, a 10.0 cm^3 sample of blood drawn from the patient had an activity of 3.0 decays/second, what is the volume of blood in the patient.

Homework Equations



A= Ao[(1/2)^(t/half life)]


The Attempt at a Solution



I have just found out the activity of after the decay, but haven't realized what to do with that number. Any help would be much appreciated.
 
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  • #2




Thank you for your question. To determine the volume of blood in the patient's body, we can use the formula A = Ao[(1/2)^(t/half life)], where A is the final activity, Ao is the initial activity, t is the time passed, and half life is the half life of the isotope.

In this case, we know that the initial activity (Ao) is 2.8x10^4 decays/second and the half life (t/half life) is 45 minutes. We also know that the time passed is 3 hours, which is equivalent to 180 minutes.

Using the formula, we can set up the following equation:

3.0 = 2.8x10^4[(1/2)^(180/45)]

Solving for the final activity, we get:

3.0/2.8x10^4 = (1/2)^4

1.0714x10^-4 = (1/16)

Multiplying both sides by 16, we get:

1.7143 = 1

Therefore, the final activity is 1.7143 decays/second.

Now, we can use this final activity in the same formula to solve for the volume of blood (V).

1.7143 = 2.8x10^4[(1/2)^(180/45)]

Solving for V, we get:

V = 2.8x10^4/1.7143

V = 16336.36 cm^3

Therefore, the volume of blood in the patient's body is approximately 16336.36 cm^3.

I hope this helps. Let me know if you have any further questions.



Scientist
 

1. What is Half-Life and how does it apply to real life?

Half-Life is a scientific concept that describes the amount of time it takes for a substance to decay by half. It can be applied to various fields such as nuclear physics, medicine, and environmental science.

2. How is Half-Life used in nuclear physics?

In nuclear physics, Half-Life is used to measure the rate of decay of radioactive elements. This information is crucial for understanding the stability and potential dangers of nuclear materials, as well as for calculating the age of fossils and artifacts through radiocarbon dating.

3. Can Half-Life be used in medicine?

Yes, Half-Life is commonly used in medicine for the administration of drugs and treatments. The Half-Life of a medication determines how long it will take for the body to eliminate half of the initial dose. This information is important for determining the dosage and frequency of a medication for optimal effectiveness.

4. How does Half-Life relate to environmental science?

In environmental science, Half-Life is used to study the decay of pollutants and toxins in soil, water, and air. By understanding the Half-Life of these substances, scientists can predict the amount of time it will take for them to break down and become less harmful to the environment.

5. Is Half-Life a constant value?

No, the Half-Life of a substance is not a constant value. It can vary depending on the specific substance, environmental conditions, and other factors. However, once the Half-Life is determined for a particular substance, it remains consistent and can be used for future calculations and predictions.

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