# Determine Half-Lives & Initial Activities of 2 Isotopes - Q&A

• Soilwork
In summary, after 1 hour in the reactor, the data shows that there were a total of 20 decays. The half-life of the short-lived isotope was 0.23 hours, while the half-life of the long-lived isotope was 0.0116 hours. The element is Antimony.
Soilwork
Q. A sample of a certain element with two naturally occurring isotopes becomes
activated by neutron capture. After 1 hour in the reactor, it is placed in a
counting room, in which the total number of decays in 1 hour is recorded at
daily intervals. A summary of the recorded data appears below.
From the data, determine the (i) half-lives and (ii) initial activities of the 2
components. (iii) What is the element?

The thing with this question is that you're given a table with the time in one column and the total number of counts in the other column.
I know that if you take the natural log of the exponential decay function that you can find lambda and therefore the half-life.
But you have to find the half-life of two isotopes and I don't know how you can do that.
Any hint that can point me in the right direction would be greatly appreciated :)

Make a graph of the log of the number of counts, versus time. What does it look like? (after mentally smoothing out any random wiggles, of course)

Yeah I get kind of two different straight lines.
The times given are as follows:
0,1,2,3,4,5,6,7,8,9,10,20,40,60,80,100,120,140,160,180,200.
So the first gradient is about 0.23 and is from the time scale of 0-10.
The second gradient is 0.0116 and is from 40 - 200.
This will give the two half lives of the isotopes, but I don't know why.
So the element is Antimony.

Soilwork said:
Yeah I get kind of two different straight lines.

That's what I suspected. The hypothetical sample started out with the number of decays being dominated by the short-lived isotope, so the initial slope reflects the shorter half-life. After most of the short-lived isotope has decayed, the decays observed are mostly from the long-lived isotope, so the second slope reflects the longer half-life.

Ahhh k thanks for that :)
So now I can just use the LOGEST function on Excel over the relevant points to find the intial activities of the two isotopes.
Thank you so much for explaining this.

## 1. What is a half-life?

A half-life is the amount of time it takes for half of a sample of a radioactive isotope to decay into a stable element. This is a characteristic property of each radioactive isotope and can range from fractions of a second to billions of years.

## 2. How do you determine the half-life of an isotope?

The half-life of an isotope can be determined through experimental measurement. A sample of the isotope is observed over a period of time and the amount of decay is measured. By plotting this data on a graph, the half-life can be calculated by finding the time it takes for the amount of the isotope to decrease by half.

## 3. What is the initial activity of an isotope?

The initial activity of an isotope refers to the amount of radioactive decay that occurs at the beginning of its decay process. This measurement is important in determining the rate of decay and the half-life of the isotope.

## 4. How can the initial activity of an isotope be determined?

The initial activity of an isotope can be determined by measuring the amount of radioactive emission from the isotope at the beginning of its decay process. This can be done using specialized equipment such as a Geiger counter or through mathematical calculations based on the half-life of the isotope.

## 5. Why is it important to determine the half-life and initial activity of isotopes?

Determining the half-life and initial activity of isotopes is important in various scientific fields, including medicine, archeology, and environmental studies. It allows for the accurate dating of artifacts and fossils, tracking the spread of pollutants, and understanding the behavior of radioactive elements in the body. This information also helps in the safe handling and disposal of radioactive materials.

• Introductory Physics Homework Help
Replies
3
Views
801
• High Energy, Nuclear, Particle Physics
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
7K
• Atomic and Condensed Matter
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
7K