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. 17-1.

The tube consists of a conducting can filled with a gas at a low pressure (approximately 0.1 atmosphere) and a thin wire carefully positioned along the longitudinal axis of the can. A high voltage (some hundreds of volts) is applied between the wire and the can. The voltage source is shown schematically in Fig. 17-1 as a battery; in most cases the actual source of voltage is an electronic power supply. The voltage is set just below the value necessary to produce an electrical discharge between the wire and the can. The end wall of the GM tube is a few thousandths of an inch thick. This thickness is sufficient to stop alpha particles from entering the GM tube, but betas and gammas can enter. If a beta particle enters the GM tube and ionizes one or more of the gas molecules in the can, positive and negative ions are produced. These ions are accelerated by the electric field between the center wire and the can and gain sufficient energy to produce more ionizations. These new ions are accelerated, produce other new ions and so on. This avalanche of ionization, in which nearly all the gas molecules in the can are ionized, provides an electric current through a resistor (R in Fig. 17-1). The voltage pulse across R is detected by an electronic counter.

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:

(1)

In the above expression, I is the radiation intensity after passing through an absorber of thickness d. The quantity I_o 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 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

(2)

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)

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

(4)

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. 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

(5)

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.