Identifying a Radioactive Material Using Half-Life Measurements

In summary, Australian post is receiving nervous attention because a parcel containing radioactive material has been delivered. The parcel is decaying at a rate of 0.25 grams per day, and inspectors are trying to identify the material. Using information from class, it is likely that an exponential equation would be a good model for radioactive decay.
  • #1
Ramandeep
6
0
the assignment is written as follows:
A parcel is attracting nervous attention at australian post. the parcel is radioactive and inspectors are trying to identify the material. Suppose they make the following measurements. There are 50 grams of the material and it's decaying at a rate of 0.25 grams per day.

One of the characteristics of radioactive materials is it's half life. That is the time it takes for half the material to decay. Below is a table giving the half-lives of common radioactive elements.

ISOTOPE HALF LIFE
Carbon-14 5730 years
Chlorine-36 301,000 years
Polonium-210 138 days
Phosphorus-32 14.2 days
Iodine-131 8 days
Uranium-238 4.5 x10years

Your task is to identify the material in the box assuming that the isotope will decrease to 25 grams. Using the ideas developed in class, it should be clear that an exponential equation would provide a good model for radioactive decay.

*******************************************
so recently in class we've been learning about derivatives, logs, ln, etcc
please help me with full detail...i have no idea how to do this
THANKSSS
 
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  • #2


In order for what you wrote, we need to assume that the material is "decaying at a rate of 0.25 grams per day" right now, now in general. Radioactive materials decay at a rate proportional to the amount, not at a constant rate. Since there is, right now, 50 g of the substance and it is, right now, decaying at a rate of .25 g per day, it is decaying at a rate of .25/50= 0.005 times the amount.

That is, if Y is the amount at any time, we have dY/dt= -.005Y. You should be able to integrate that to get Y as an exponential. Then determine the time, in days, until there is exactly half left. That will give you the half life.
 
  • #3


Thankyou so much because that was really helpful. Ecspecially the first paragraph because it certified the calculations I had! Though I could not understand how to get half life of the suinstance still... So could you please just explain in more detail... This is all new to me, maths is not my forte haha.
Thanks :)
 
  • #4


Substance / material ****
 

Related to Identifying a Radioactive Material Using Half-Life Measurements

1. What is half-life and how is it used to identify radioactive materials?

Half-life is the amount of time it takes for half of the radioactive atoms in a sample to decay. By measuring the half-life of a material, scientists can determine the rate of decay and use it to identify the type of radioactive material present.

2. What instruments are used to measure half-life and identify radioactive materials?

The most commonly used instrument is a Geiger counter, which measures the radiation emitted from a material. Other instruments include scintillation counters and gamma spectrometers.

3. Can half-life measurements be used to determine the level of radioactivity in a sample?

Yes, half-life measurements can be used to calculate the specific activity of a material, which is the amount of radiation emitted per unit mass. This can help determine the level of radioactivity present in a sample.

4. How accurate are half-life measurements in identifying radioactive materials?

Half-life measurements are highly accurate and precise, with only a small margin of error. However, the accuracy depends on the quality of the instrument used and the skill of the person conducting the measurements.

5. Are there any safety precautions that need to be taken when measuring the half-life of a radioactive material?

Yes, it is important to follow proper safety protocols when working with radioactive materials, including wearing protective gear and handling the material in a designated area. It is also important to properly dispose of the material after the measurements have been taken.

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