Experiment 18

Experiment 18 THE EFFECT OF DISTANCE ON INTENSITY OF RADIATION

PRELAB

PURPOSE

To determine how the count rate from a source of nuclear radiation varies with the distance from the source.

EQUIPMENT Nucleus^® counter, Geiger-Mueller tube with stand, radioactive source.

RELEVANT EQUATIONS

Intensity vs. Distance

DISCUSSION

The Geiger-Mueller tube and the scaler operation are discussed in Experiment 17. Read this discussion if you have not already done so. 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 N_T 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

(1)

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

(2)

The quantity N_T is determined by the source and A is fixed by the detector used. For a given experiment, these quantities are fixed and we see that

(3)

In other words, the count rate varies inversely with the square of the distance from the source.

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. 18-1 illustrates these quantities.

Figure 18-1: Geometry of a Point Source and the GM Tube Window

Experimentally, we measure d, not R. Since R² = d² + a², where a is the radius of the GM tube window, equation (3) should be written as

(4)

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.