# Episode 315: The inverse square law

Lesson for 16-19

- Activity time 70 minutes
- Level Advanced

This episode considers the ways in which the intensity of radiation decreases with distance from the source.

Lesson Summary

- Demonstration and discussion: radiation spreading out, and an analogy (20 minutes)
- Worked example: Thinking in proportions (5 minutes)
- Student experiment: Estimating the power output of the sun (15 minutes)
- Student questions: Comparing lamps (30 minutes)

## Discussion and demonstrations: Radiation spreading out and an analogy

Set up three simple demonstrations:

- Bright lamp and phototransistor or other light meter
- Microwave source and detector
- Gamma ray source and Geiger counter

Show that the intensity of each type of radiation decreases with distance from the source.

(If students have already studied radioactivity, they may be aware of the inverse square law for gamma radiation.)

Why does the intensity decrease with distance? Try to give two general reasons. (Absorption and spreading out.)

Radiation spreading out radially covers a bigger and bigger area, proportional to r^{2}, so its intensity decreases as 1*r*_{2}. It can help to think of a toast-buttering gun

. The gun can butter a single slice of toast at a distance of 1 m. How can it butter four slices simultaneously? (Place them in a 2 × 2 array at a distance of 2 m.) How thick will the butter be? (14 of original thickness.) Extend this to a 3 × 3 array at 3 m, and so on.

Point out that the intensity of radiation can be measured in watts per square metre (W m^{-2}).

## Worked examples: Thinking in proportions

A cobalt-60 source gives a gamma dose rate of 160 μSv h^{-1} at 1.0 m away. At what distance will the dose rate be 40 μSv h^{-1}?

Answer: If the intensity has gone down by a factor of 4, the distance away must have doubled to 2.0 m.

Or by

*I* = *k**d*^{ 2}

*I*_{1}*I*_{2} = (*d*_{2})^{2}(*d*_{1})^{2}

## Student experiment: Estimating the power output of the sun

Students can make measurements to estimate the power output of the sun, making use of the inverse square law. Note that there is a good opportunity here to discuss the validity of the answer obtained.

Episode 315-1: Summer sun remembered (Word, 54 KB)

## Student questions: Comparing lamps

Some calculations.

Episode 315-2: Comparing intensities for lamps (Word, 26 KB)