Introductory Laboratory Category
Low Cost Category

2002 AAPT Apparatus Competition, Boise State University

Name: Alice and Richard Flarend

Address: Bellwood-Antis High School Penn State Altoona

400 Martin Street 3000 Ivyside Drive

Bellwood, PA 16617 Altoona, PA 16601

Phone: 814-949-5744

Fax: 814-949-5011

E-mail: amf@tuckahoe.blwd.k12.pa.us ref7@psu.edu

Apparatus Title: Radioactive Decay and Daughter Build-up Simulation

Abstract (40-50 words)

Students ‘roll’ two hundred wood cubes in a self-contained box to simulate randomized radioactive decay. The cubes which decay are then replaced with either ‘stable’ or ‘radioactive’ daughter cubes. This lab is an improvement over other decay simulations because it addresses several misconceptions students often have with radiation which other simulations do not address.

Equipment required to construct apparatus:

Item	Source	Part number	Bulk Cost	Unit cost	Number	Cost
1/2” wood cubes	Kemp Enterprises	CUBE-1/2	$73.00/5000	$0.0146	200	$2.92
5/8” wood cubes	Kemp Enterprises	CUBE-5/8	$140.00/5000	$0.0280	200	$5.60
3/4” wood cubes	Kemp Enterprises	CUBE-3/4	$146.00/5000	$0.0290	200	$5.80
4-cup Ziplock disposable containers	K-mart	02570010880	$2.99/4	$0.75	2	$1.50
#2 ‘Martha Stewart’ clear storage bin	K-mart	76201608845		$4.49	1	$4.49
red spray paint*	Family Dollar			$1.00	1	$1.00
blue spray paint*	Family Dollar			$1.00	1	$1.00
			Total Cost (per station)			$22.31

*In retrospect, it is better to use high quality spray paint which will give a very brilliant finish than the cheaper paint which gives a faded appearance. The faded appearance is more difficult to distinguish from some of the darker non-painted cubes with just a quick glance.

Description:

Preparation:

In the outdoors, the large wood cubes are laid out in a closely packed arrangement on a flat surface so that it is convenient for just the tops to be painted blue (the cubes on the edge may need to be masked to prevent the sides from being painted). After drying, the cubes are all flipped over and painted on the opposite side. This is easily accomplished using student labor in a surprisingly short amount of time.

The medium cubes are painted red on only one side using the same method. The small cubes are not painted.

The cubes are divided up into 20 separate lab setups/stations with 200 large cubes, about 160-175 medium cubes, and about 200 small cubes per station. The large cubes are the only ones which need to be counted out individually, and they are placed in the storage bin. One 4-cup Ziplock container packed in a very orderly fashion will contain enough of the medium cubes for each station (this can be accomplished by vibrating the container as the cubes are slowly pored in.) The other 4-cup Ziplock container has plenty of room for 200 of the small cubes, and they can be quickly counted by mass using a scale reading 1 or 0.1 grams

When not in use, each lab setup stores compactly, with the two smaller containers placed on top of the large cubes inside the storage bin.

Because the cubes are self-contained in the bin, this lab can be accomplished without the use of a large laboratory table or other dedicated space.

General directions:

The wood cubes represent either stable or unstable nuclei. When ‘rolled,’ a cube is decays if its painted side is facing up. The large cubes decay into the medium cubes, and the medium cubes decay into the smaller cubes which are stable.

Start with only the 200 large cubes in the bin. The cubes are ‘rolled’ by placing them in the large bin and shaking (Need we say with the lid on??). Remove the lid, and carefully remove all the large cubes which have decayed. Count the decayed large cubes, set them aside, and replace them with the same number of medium cubes in the bin.

Shake again. Now remove all the large cubes and the medium cubes which have decayed. Separate the two sizes of decayed cubes, count them, set them aside, replace the medium decayed cubes with small cubes, and replace the large decayed cubes with medium cubes (it is fine to re-use the decayed medium cubes).

Repeat the above step about 15 times.

It is surprising that most students will end up with some number of cubes other than 200 no matter how simple you try to make the directions. But it is certainly the case that it is easier to count the cubes removed than to count the cubes remaining after each shake. A simple spreadsheet allows the student to just enter the number of cubes removed of each size and then the spreadsheet can then calculate the remaining cubes and generate whatever graphs are desired.

Misconceptions:

Each shake is NOT deemed to be a half-life (as it would be with flipping coins), but rather an arbitrary length of time. Thus the student sees that in each shake, the number of radioactive nuclei is decreasing, but not by 1/2 for each unit of time. The half-life for each of the two radioactive nuclei depends on the probability of decay (1/3 or 1/6) so that the half-life of the large and medium cubes is about 1.5 ‘shakes’ and 3 ‘shakes’ respectfully. (Note: The real half-lives would be a little longer than the 1.5 and 3 ‘shakes’, but that detail can be left to the more advanced student.)

Students usually believe than when a nuclei decays, that it just vanishes. This simulation reinforces the notion that radioactive nuclei just change into either other radioactive nuclei or into stable nuclei.

The size and mass of the cubes is continually decreasing while the total number of cubes remains constant. This address the mass-energy equivalence which is so critical in nuclear physics. Although the decrease in mass is exaggerated by about 10,000 times.

Comments about Materials:

The large “#2 Martha Stewart Clear Storage Bin” was chosen after spending quite some time in the storage aisle of the local K-mart. No other container has a nice flat bottom, relatively square edges (minimizing cubes laying on their corners), and a size which allows a good compromise between compact storage and a large bottom so all the cubes to be easily seen after each shake. Thus this particular container was chosen quite specifically.

We first tried to obtain dice in bulk quantities, but this proved to be very expensive. The wood cubes use here are available in bulk for a reasonable price and are much cheaper than bulk quantities of dice. These cubes are available in small quantities at retail craft stores, but the price is prohibitive for using large numbers of the cubes. Purchasing the case sizes we did will cost about $400 plus shipping, but will give you enough materials for 25 stations. Kemp Enterprises also sells smaller cases of the 5/8” and 3/4” cubes with 2500 in each so you only need to spend about $240 plus shipping for about 12 stations. Or, you can pay broken case fees and order even less.

You could also purchase only one size of cubes and create several nuclei from that one size. But this makes separating the cubes much more difficult and does not address the mass-energy equivalence as discussed above.

Sketch (computer generated if possible):

Compact storage of entire lab setup.

Shaking the nuclei to see which ones decay.

Picking out the decayed nuclei.