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Inverse Square Law
Objectives:
- Learning how to calculate the current activity of radioactive sources theoretically.
- Verifying the inverse square relationship between the distance and intensity of radiation.
Theory:
Determining the Current Activity of the Radiation Sources by
calculation:
To calculate the efficiency of the tube we therefore need to know the number of radiation particles emitted by the source in some unit of time. This is the “activity” of the source. But this is not the activity that is written on the source on the day of its production, because the activity of the radiation sources decreases over time following production of the samples, it is therefore necessary to compute the current activity of each sample in decays per minute. The activity (A) at time (t) is given by the equation
( ) (1) Where: Ao is the activity at time of production λ is called the decay constant and is given by = ln 2 / t½, where t½ is the half‐life of the source radiation. Equation (5) can be written as:
The activity that we will find using equation 6 will be in micro Curies and will need to be converted to decays per minute (dpm) to be comparable to the count rate that we will measure in our readings. To do so remember that:
i.e.:
Inverse square law of radiation:
As a source is moved away from the detector, the intensity of radiation, and therefore the amount of detected radiation, decreases. You have observed many similar effects in your life. The farther you move away from a friend, the harder it is to hear them. Or the farther you move away from a light source, the harder it is to see. Basically, nature provides many examples (including light, sound, gravity, electric force and radiation) that follow an inverse square law. What the inverse square law basically says is that if you move to a distance d away from the window of the GM counter, then the intensity of radiation decreases by a factor 1/d^2.
To see why the situation is as such let us assume that we have a radioactive source that emits particles at a rate of A particles/minute. It is reasonable to assume that these particles are given off in an isotropic manner, that is, equally in all directions. If we place the source in the center of a spherical shell of radius d, it is quite easy to measure the number of particles per minute for each cm^2 of the spherical shell. This is called the intensity and is given by (see figure 2):
( )
The number of counts per minute that we measure in our experiments is actually proportional to the intensity and therefore
appropriate shielding. Lead is a potentially toxic material if it inters the body by swallowing or breathing its dust and if the exposure is long term. DO NOT touch your face or put your hands in your mouth after touching the lead bricks used for shielding. Always wash hands before leaving the lab.
Procedure:
- Connect the plugs to the electric mains and switch the ST 150 station ON.
- Set the timer to 60s and the voltage to the operating voltage found in first lab.
- Record the count rate per one minute for the back ground (IB.G) 2 times and take the average.
- Ask your instructor for a gamma source and note down all the info on the source label and place it under the GM tube on the top shelf.
- Record the count rate 2 times and find the average count rate of the source.
- Move the source one shelf down and repeat step 5.
- Repeat step 6 for all the remaining shelves.
- plot a graph that would verify the inverse square law of propagation of radiation.
- Calculate the time t that has passed since the fabrication of the source. 10.Calculate the current activity of the source using equation (2)
Data Sheet
InverseSquareLa w
Source description
Date of Calibration
Half life (t 1 / 2 ) ( ……)
Activity (A 0 ) Element ( ……. )
Data:
IB.G = (……..+.……)/2= ……….. (….…).
I 1
I 2
Iav (….....)
I=Iav – IB.G (.…….)
