Radioactive or not?

We looked at the question of whether "receiving radiation" will cause an object to become radioactive.

On Friday I set the tangerine down onto 3 radioactive disk sources, which in turn were placed on top of the somewhat radioactive piece of fiestaware.

The following Monday. We removed the disks and tested the bottom, the part closest to the radiation sources. I counted for an hour, with 1-minute long counts. (60 "samples")

Below is the data: The statistics say the average counting rate was 16.8 CPM, and the standard deviation was 5.0 CPM. So, I would talk about the average count rate as: 16.8$\pm$5 CPM.

Here is the $\pm 1\sigma$ "uncertainty bar" for the tangerine measurement superimposed on the day-long background counting data:


But on more careful reflection we decided to measure the radiation without the piece of cardboard. It was also 30-40 CPM!

After moving the radioactive disks further away, Counting for 3 minutes with nothing nearby gave us 22+22+13 = 57 counts in 3 min. This was 57/3=19 CPM which does lie in the range 16.3$\pm$4.1 CPM.

Counting again for 3 minutes, we found:

  • Banana : 52 counts : 52/3$\approx$17.3 CPM
  • Cardboard : 50 : 50/3$\approx$16.7 CPM.

Because these values are both in the $\pm \sigma$ range of the background data, we concluded that neither the banana skin, nor the cardboard were radioactive, or at least no more so than the amount of "background" radiation.

Another test: KCl or NaCl?

You are a geologist out for a hike. As you come over a ridge, you spot these beautiful salt flats. You know that potassium-chloride (KCl) is mildly radioactive, but sodium chloride (NaCl) is not, so you wonder which kind of salt this is.

You happen to have brought your geiger counter with you! So, you let it sit beside some of the salt for a while.

Here is the data you recorded.

Each time a radioactive nucleus decays, it gives off a particle, or a short burst of energy. The geiger counter "clicks" each time it receives one of these. So, you can count the number of "clicks" received in a minute (Counts per minute = CPM or "clicks per minute") by the geiger counter.

You have left the geiger counter running for 40 minutes. Each minute, you've recorded how many clicks there were in that minute. The geiger counter is clicking. The sample looks radioactive! But wait, there's more to it than that...

Background radiation

Even when there's no source of radiation nearby, a geiger counter will still click. We say, this is because of the background radiation.

Sources of background radiation include small amounts of radioactive potassium in everyone's bodies, trace amounts of Radon gas given off by mineral deposits all over Earth, and cosmic rays coming from outside our solar system.

To know if your salt is radioactive, you need to know if the geiger counter clicks *more* when it's close to the salt than the background radiation (as measured someplace where you are pretty certain there is nothing radioactive nearby).

On your way home, after you've climbed out of the valley, and there's no salt (or radioactive disks) around, you take some measurements of the "background" radiation: You make 40 measurements, each time counting the number of clicks in one minute. We'd like to find the average number of clicks per minute (call this CPM${}_{\text{ave}}$), and the standard deviation of the clicks per minute from the average, $\sigma$ (units are also CPM).

Visually estimating the average and standard deviation

With 40 measurements, we'd expect 70%, or 0.7*40=28 of the counts to be in the "1 sigma interval"--between CPM${}_{\text{ave}}+\sigma$ and CPM${}_{\text{ave}}-\sigma$. And so 40-28=12 measurements will lie outside that range.

12 measurements should be outside the range, so about 6 above, and 6 below. I put a ruler on the plots, and find that if it's at 84.5 clicks/min I'll get exactly 6 points above the line.

Similarly, drawing a line at about 57.5 leaves 6 points below the line.

Background radiation results: My average should be close to the center of the region. I'll just average my high and low lines to get: $$\text{CPM}_\text{ave} \approx \frac{57.5+84.5}{2}=71 \text{ CPM}.$$

The width of that band between the upper and lower line is $2*\sigma$. So, $$\sigma = \frac{84.5-57.5}{2}=13.5 \text{ CPM}.$$

And I'd report the background radiation as $71.0\pm 13.5$ CPM.

Now your turn! Use the same technique to estimate the average, and standard deviation from the salt data.

  • Print this answer sheet, draw the lines on that sheet, and answer any other questions, and hand/scan that in as your homework assignment.

Here again is the salt data (40 measurements). Draw the lines such that about 12 points (~6 above and 6 below) are excluded. Use your lines to estimate:

CPM${}_{\text{ave}}$=________ CPM.


$\sigma=$________ CPM
Does the $\pm$1 standard deviation interval for the salt overlap the 1 standard deviation interval of the background radiation (right) measurement or not?


What can you say about whether your salt sample is emitting more radiation than the background radiation, or not?


Photo credit: Dave R