Absorption with tape

What the Activity is for

A series of measurements showing exponential decay.

As you add a thickness of absorber, so the power in a beam decreases by a constant fraction. This leads to an exponential decay of the power in the beam.

Exponential decays (which are just constant fractional decays) will be met several times in radiation and perhaps be of particular interest when studying ionising radiation.

What to Prepare

• an optical light sensor
• a light source
• a microscope slide
• lengths of ghost, or mending tape

What Happens During this Activity

You will need to do some trial work, in order to match up the best distances with the sensor and light source that you choose.

This is best done as a student exploration. Skilful experimentation on the part of the student will give a truly beautiful exponential curve. You will have to guide the students as to how to set up the apparatus, so it's best not to call it an out and out investigation. The other reason for not labelling it an investigation is that the outcome is known – we are after a particular pattern here, and you should challenge all students to get it.

Students record and plot the power transmitted by increasing thicknesses of tape. The microscope slide is used to hold the tape. Emphasise adding one thickness of tape at a time. The question to explore: what happens when you add a single thickness of tape? That is, what's the pattern here? You could amplify the question either in terms of the power in the beam, the number of photons in the stream, or just in terms of the brightness. Decide on an approach well-matched to your class.

Students should be encouraged to explain in their own words the shape of the graph. A useful trick is to imagine that you have to tell your friend what you have found without being able to show them – how could you get them to draw the graph you have in front of you just by telling them about the shape (and not about the particular values that you happen to have got)?

How far you go in exploring the pattern here will depend on the aptitude and interest of the class, but we think it's useful to meet the exponential pattern as a variation with distance first because it's more obvious what is going on than for variations over time. You can step forwards as well as backwards through the pattern without extraneous difficulties, for example.

You can repeat the experiment as a demonstration, and use this to pull out the main points, by using microwave (3 cm) apparatus and textbooks for the incremental thicknesses. Choose your textbook wisely, so that 6 to 8 textbooks will decrease the power detected to a very low value. You might choose to use software to plot the values as you go. Indeed, you might use a data analysis program to explore the constant fractional nature of the decay. There's a lot here: choose the depth of treatment to suit the class.