EFFECTS
OF THICKNESS & DISTANCE
INTENSITY
OF RADIATION
PRELAB
PURPOSE
To determine the effect of the thickness of an absorber and source distance on the intensity of radiation.
EQUIPMENT Vernier radiation monitor with interface, micrometer caliper, half-meter stick, support, plastic and lead absorbers of various thickness.
RELEVANT EQUATIONS
Variation of Intensity with Thickness:
Intensity vs. Distance:
DISCUSSION
The Geiger-Mueller tube and the associated electronic circuitry will detect and count the passage of ionizing radiation such as alpha particles, beta particles, and gamma rays. The tube construction is shown schematically in Fig. 2.17-1.
Meanwhile the potential difference between the wire and the can has been reduced to a small value -- much lower than the value required to maintain the discharge. The positive ions are neutralized by touching the can and the voltage across the wire-can electrodes will build up again to a value just below the value necessary to create discharge. While the voltage is building-up, the tube will not respond to the passage of a charged particle through it. However, this "dead time" is short and we will not need to take it into account in our experiment.
The number of counts in any time interval depends on how well the GM tube can be ionized when radiation enters it. Gamma quanta are counted with a low efficiency, about one-percent. Beta particles can be counted with an efficiency close to 100%. Since our GM tubes will not admit any alpha particles at all, we cannot use these counters to detect this type of radiation.
In this experiment you will study the way that the radiation counts from a radioactive source as detected by the G-M tube vary with both thickness of absorbing materials and distance from the source.
Variation with Absorber Thickness
The radiation intensity varies with the thickness of the absorber exponentially. The relation that describes this variation is:
In the above expression, I
is the radiation intensity after passing through an absorber of thickness
d.
The quantity Io is the radiation
intensity entering the absorber. The factor a
is called the absorbtion coefficient and depends upon the material used.
Variation with Distance
A point source emits equally well in all directions. If we could detect all particles emitted in one second from a point source, this number would be the same no matter how far away from the source our detector is located. This detector is imagined to completely surround the source. If NT represents the total number of particles per second detected over a spherical surface of radius R, then the number of particles per unit area will be:
Since a real detector is limited in size, we suppose the real detector has an opening to allow particles to enter. This opening has an area, A. Thus, the number of particles that enter the detector and are counted is:
(3)
A closer inspection of the experimental set up suggests that the following modification in analysis may improve the results:
Let d represent the vertical distance from the point source to the GM tube window (as measured from the edge of the tray holder to the bottom of the GM tube stand), and let R be the radial distance from the source to the outside perimeter of the window (do not attempt to measure this distance). Fig. 2.17-2 illustrates these quantities.
Experimentally, we measure d, not R. Since R2 = d2 + a2 , where a is the radius of the GM tube window, equation (4) should be written as:
The naive approach would suggest using
d as the distance from the source to the detector. However, it is
clear that at small distances like we will use in this experiment
the size of the detector and its finite area should be taken into account.
You will do this in the ANALYSIS section.