Figure out the activity of a radioactive sample?

[jumbogala]

Homework Statement

The sample is placed 0.12 m beneath a Geiger counter.

The counter registers 2 counts per second. What is the activity of the sample?

Homework Equations

The Attempt at a Solution

Just a guess. I am making up formulas here so please tell me if they're not even true.

(2 counts/s)/(2E-4 m²) = Intensity = 10 000 counts/s/m²

Then multiply this by the distance to get the activity? So this would give 1200 counts/s?

Is that correct?

 

[gneill]

Do you suppose that all the particles emitted by the sample are being captured by the Geiger counter?

 

[jumbogala]

Nope, they're not. But I don't know how to account for that, since I have no idea what percentage are.

 

[gneill]

Nope, they're not. But I don't know how to account for that, since I have no idea what percentage are.

What if you assumed that the sample emits uniformly in all directions?

 

[rwisz]

Your attempt at a solution is close, but there are a few issues with the equations you have used. Let's break it down step by step:

1. First, we need to understand what is meant by "activity" in this context. In the field of radioactivity, activity refers to the rate at which a radioactive sample decays, measured in units of becquerels (Bq). One becquerel is equal to one decay per second. So, the activity of a sample can be thought of as the number of decays that occur per unit time.

2. The equation you have used to calculate intensity is not quite accurate. Intensity is a measure of the number of particles passing through a unit area per unit time. In this case, the particles are the decaying atoms from the radioactive sample, and the unit area is the surface of the Geiger counter. So, the correct equation for intensity would be:

Intensity = (2 counts/s)/(0.12 m2) = 16.67 counts/s/m2

3. Now, to calculate the activity, we need to take into account the efficiency of the Geiger counter. This is because not all of the decaying atoms from the sample will be detected by the counter. The efficiency of a Geiger counter is typically around 10-30%, so let's assume an efficiency of 20%. This means that only 20% of the decays are being detected by the counter. So, the equation for activity would be:

Activity = (Intensity) x (Efficiency) = (16.67 counts/s/m2) x (0.20) = 3.33 counts/s/m2

4. Finally, we need to convert this to the correct units of becquerels. Remember, one becquerel is equal to one decay per second. So, we can simply divide the activity by the number of counts per second to get the activity in becquerels:

Activity = (3.33 counts/s/m2) / (2 counts/s) = 1.67 Bq

Therefore, the activity of the radioactive sample is 1.67 Bq.

In summary, your intuition was correct in that we need to use the intensity and distance to calculate the activity, but we also need to take into account the efficiency of the detector and convert to the correct units of becquerels.