An Investigation into Gamma Rays and the Inverse Square Law.

Introduction:

As with any radiation source, the radiation emitted spreads out from the origin (the point source). Although the gamma source to be used is not strictly a point source it is a fair approximation of one and will be sufficient for use in this experiment. The intensity of the radiation diminishes with the square of the distance if there is no absorption by the medium. Gamma radiation is absorbed by air molecules but may be considered negligible.

Background Information and Research:

Supplied by the centre for non-destructive evaluation, Iowa state university, Ames, IA-

-Newton’s inverse square law: Any point source, which spreads its influence equally in all directions without a limit to its range, will obey the inverse square law.

The intensity of the influence at any given radius(r) is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound and radiation obey the inverse square law.

E.g.: - All measures of exposure of a point radiation source will drop off by the inverse square law.

If the radiation exposure is 100mR/hr at 1 inch from a source, the exposure will be 0.01mR/hr at 100 inches.

The inverse square law is a principle that expresses the way radiant energy propagates through space. The rule states that the power intensity per unit area from a point source, if the rays strike the surface at right angle, varies inversely according to the square of the distance from the source.
The intensity of light observed from a ...

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E.g.: - All measures of exposure of a point radiation source will drop off by the inverse square law.

If the radiation exposure is 100mR/hr at 1 inch from a source, the exposure will be 0.01mR/hr at 100 inches.

The inverse square law is a principle that expresses the way radiant energy propagates through space. The rule states that the power intensity per unit area from a point source, if the rays strike the surface at right angle, varies inversely according to the square of the distance from the source.
The intensity of light observed from a source of constant intrinsic luminosity falls off as the square of the distance from the object. This is known as the inverse square law for light intensity. Thus, if I double the distance to a light source the observed intensity is decreased to (1/2)2 = 1/4 of its original value. Generally, the ratio of intensities at distances d1 and d2 are
The inverse-square law

A source of light will look dimmer the farther it is. Similarly the farther away a star is the fainter it will look; using geometry we can determine just how a star dims with distance

Imagine constructing two spheres around a given star, one ten times farther from the star than the other (if the radius of the inner sphere is R, the radius of the outer sphere is 10 R). Now let us subdivide each sphere into little squares, 1 square foot in area, and assume than on the inner sphere I could fit one million such squares. Since the area of a sphere increases as the square of the radius, the second sphere will accommodate 100 times the number of squares on the first sphere, that is, 100 million squares (all 1 square foot in area). Now, since all the light from the star goes through both spheres, the amount of light going through one little square in the inner sphere must be spread out among 100 similar squares on the outer sphere. This implies that the brightness of the star drops by a factor of 100, when we go from the distance R to the distance 10 R (see Fig. ).

Hypothesis:

Using the facts about the inverse square law, it can be assumed that the count rate (C), from a gamma point source, would follow the theory:

C ∝ 1/x2 (where x = the distance from the source)

However the probe creates a problem in the fact that x is not precise, as it cannot be measured directly. If the un-measurable section is referred to as d, the expression becomes:

C ∝ 1/(x+d)2 or C = k/( x+d)2 (Where k is a constant)

(x+d)2 = k/C

Rearranging this gives: