Measure. Analyze. Learn.
I'm John Gastineau, staff scientist, and physicist
with Vernier Software and Technology.
I'm going to show you one of the experiments
from the "Nuclear Radiation with Vernier" Book.
This is a very short book. It just has six activities in it.
It can be used either with a chemistry
or physics laboratory course.
The activity I'm going to show you,
is the Counting Statistics Activity.
Nuclear Counting statistics can be described either by
Poisson or Gaussian statistics depending on
the number of Counts per unit time.
So, I'm going to take a strontium 90 source,
and put it right up against the Geiger tube
in a Vernier Radiation Monitor.
I've already done some setup in Logger Pro.
I'll go through how that setup is done in just a little bit.
I have chosen a Count interval so that on average only one or
two decays are captured during any single Count interval.
And, if I take data, I see two graphs.
One, is the number of Counts per unit interval
as a function of time, and you see that's just kind of a noisy
number. It's a small number, 0, 1, 2, something like that.
The lower graph is a histogram of those
Counts per time interval.
And, you can see, in the left hand bar, is the 0 count bar.
That shows that some of the time,
there are no counts at all during a time interval.
The most common result is to have
one Count during a time interval.
I end up with a distribution that is asymmetric.
This is a Poisson distribution.
Now, I can change my count interval, so that the number of
Counts during one interval is instead about 15 to 20.
If I do that, the Counting statistics will be
described well by Gaussian statistics.
So, I'm going to go in and change my count interval.
You can see here, that it had been
set down to about 2 milliseconds.
I'm going to change that to 30 milliseconds.
And, I'm going to click "Done"
And, I'm going to clear my old data here, and take a fresh run.
This time the average number of
Counts in a time interval is approximately 16 to 17.
And my distribution of Counts is symmetric,
And, the shape of it is very much that of a Gaussian.
The longer I take data,
the more closely that approximates a Gaussian.
Now, I took data all night last night
to show what it would look like
if we counted for over 40,000 time intervals.
Let me show you what that one looks like.
And, the graph at the bottom of the screen
is a histogram of my / of the Count frequency.
The average number of counts in an interval,
in this case, was up around 570.
But, you can see the shape of
the distribution is that of a Gaussian.
The black line is a Gaussian curve fit,
that I have applied in Logger Pro.
Also showing that this distribution approximates a Gaussian.
So, let me show you how I set this up.
This is my Strontium 90 source.
I'm going to need to put that back by the radiation monitor,
but I have a Vernier Radiation Monitor.
It's a simple Geiger tube.
I've got that connected to the digital port
on a Vernier LabQuest mini. We could also use a LabQuest 2.
I'm running Logger Pro on my computer.
And, I'm going to open a file that is included
with Logger Pro for the Counting Statistics activity
in the "Nuclear Radiation with Vernier" book.
So, let me open that file.
The first thing that I need to do to conduct this experiment
is to find a time interval in which I get
on average only about 1 or 2 Counts.
To set that time interval, I need to measure the
average rate of my radioactive source.
So, I'm going to put that right next to the radiation monitor.
And, this file is set up to take data once every second.
And, it gives me then the number of Counts,
in a one second interval.
I can see looking at my screen that my average number of
Counts is somewhere just over 500 counts in a 1 sec. interval.
That means that if I were to use a 2 millisecond Count interval,
I should on average, get about one Count.
I think when I'll do this experiment,
I'll set it up to use 3 milliseconds.
So, I'll get an average just over 1 Count per interval.
To do that, I'm going to go to my data collection dialog.
That is the icon, right next to the collect button,
that looks like a stopwatch.
And, you can see the seconds per sample setting
is currently set to 1 second.
I'm going to change that to ".003", or 3 milliseconds.
And tap OK {"Done"}.
Let me clear the data here.
And, I'll start taking data again.
This time, my Count intervals are very short,
just 3 milliseconds long.
And so, I've got a lot of them going past.
And you see that nice Poisson distribution
growing in the histogram.
To collect the Gaussian distribution,
I need to increase the duration of the count interval
to get an average count rate of something more than 15.
So, to do that, let me stop that.
And, go back to the seconds per sample field,
and let me change that.
Let's see, my average was, here was a little over 2,
so let me just multiply that by 10.
So, I'll set it to .03.
And clear data.
So now, I'll collect data using this longer time interval.
With the higher average number of Counts per time interval.
The distribution of the Counts per time interval
follows a Gaussian distribution.
So, that's all there is to studying Counting Statistics
using the Vernier Radiation Monitor and Logger Pro.
For more information on this activity, or any of
the other activities in "Nuclear Radiation with Vernier"
check out the Vernier website.