The Inverse Square

In 1896, Henri Becquerel accidentally discovered radiation while working with photographic film and natural radioactive materials like radium and uranium. Since then, our understanding of radiation has expanded significantly. In this experiment, we will explore how radiation intensity changes with distance using a completely safe beta particle emitter.

Radiation travels outward in straight lines from its source, much like sunlight. As it spreads out, its intensity decreases. This behavior follows the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source. To further analyze this relationship, we will measure radiation intensity at five distances.

Objective   

 To explore and calculate the relationship (if any) between the distance from radioactive sources and the intensity of beta radiation.                                       

Procedure

1. Place down a long strip of tape and measure 0cm, 8cm, 16cm, 32cm, and 48cm. Mark those points using a marker.

2. Place your radiation source at the 0cm point making sure it's placed upright or facing your Geiger counter.

3. Put the Geiger counter in a comfortable spot. If your counter has a built-in radiation source, then put it further away to reduce error.

4. Record the background activity before starting.

5. Place the counter on the tape, 8cm from the radiation source.

6. Wait until the counter is stable and record the counts-per-minute, perform 3 trials.

7. Repeat steps 5 and 6 while moving your counter to the other points.

8. Calculate the average between the 3 trials for each point.

9. Find the standard deviation of all of the trial averages.

10. Square the distances and divide those by 1 and multiply it by the average rate of the first data point to find the prediction of the average (cpm). 

11.  Lastly, calculate the difference with predicted - average. Record all of this in using Google Sheets. You can use the formula function with the equal sign (=).

Questions:

1. Why was the background activity recorded for this experiment? 

2. What is the source of the background activity?

3. Would the background activity be the same taken at sea level as taken on top of a mountain? Explain.

4. What happens to the intensity of radiation activity when the distance between the Geiger counter and source is 4x greater than the initial distance? How about 3x?

5. According to the inverse square law, when the distance is doubled from 8 cm to 16 cm the reading should decrease to 1/4 its initial reading. Do your data calculations agree with the inverse square? Explain why or why not.

6. Explain how distance and radioactive materials are potential hazards to you.

7. Interpolate the number of counts for the radiation source at a distance of 12 cm.

Optional: 

1. Evaluate how background activities may influence your data.

To access data from our own trials, click here.