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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. This comes from strictly geometrical considerations. 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.

As one of the fields which obey the general inverse square law, a point radiation source can be characterized by the diagram above whether you are talking about Roentgens, rads, or rems. All measures of exposure will drop off by the inverse square law. For example, if the radiation exposure is 100 mR/hr at 1 inch from a source, the exposure will be 0.01 mR/hr at 100 inches.

The applet below shows a radioactive source. The distance to the green source is shown below. You can also drag the little person and his Geiger counter around to a distance of your choice. When the mouse button is released, a point is plotted on the graph. The dosage the person receives at the particular distance is shown numerically and graphically. The graph allows you to confirm Newton's Inverse Square Law.

If the distance is too small, the dosage will be too high and our brave technician will face severe medical effects. To clear the graph, select a new material, or the same one again. Moving the mouse from the white area to the gray will turn off the sound!

What dosage in mR/hr is considered safe? Better find out!
The red dosage lines represent 2, 5, and 100 mR/hr levels.

Exercise: Assume you are standing three feet from a a 15 Curie cobalt-60 source. How many mR/hr dosages are you getting?