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An Investigation into Gamma Rays and the Inverse Square Law.

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Introduction

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.

...read more.

Middle

image00.png                                                                                                                                  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                                 image01.png

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

Figure 8.1: Illustration of the inverse-square law: all the light trough the 1 square-foot first area goes through the second one, which is 100 times larger, hence the light intensity per square foot is 100 times smaller in the second area. The intensity drops as 1/R2.  

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Conclusion

R to the distance 10 R (see Fig. 8.1). image02.png

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:

X = √k/C – d

If the inverse square law is followed, a graph of distance against the reciprocal of the count rate should be a straight line.

Apparatus:

  • Rad-meter (used because of accuracy)
  • Gamma source (
  • Ruler

...read more.

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