Creative Education

2012. Vol.3, No.5, 671-673

Published Online September 2012 in SciRes (http://www.SciRP.org/journal/ce) http://dx.doi.org/10.4236/ce.2012.35099

Copyright © 2012 SciRes. 671

Radioactive Branching Using Dice

Sarmistha Sahu

Department of Physics, Maharani Lakshmi Ammanni College for Women, Bangalore, India

Email: sarmistha.sahu@gmail.com

Received July 7th, 2012; revised August 12th, 2012; accepted August 22nd, 2012

Dice rolling (Emeric, 1997) is a useful pedagogical tool (Arthur & Ian, 2012; Todd, Clifton, Ingrid, &

Zdravko, 2006) to introduce students to the concepts and essential features of radioactivity. It can be ex-

tended to explain radioactive branching. In the process, the students learn about half life, decay constant

and activity of a radioactive substance. Terms like stochastic processes, probability of decay, statistical

fluctuations, and mutually exclusive processes; becomes clear in this process.

Keywords: Radioactivity; Probability; Transition Rate; Half Life; Radioactive Branching

Introduction

Dice rolling is being used as a pedagogical tool in schools as

well as undergraduate studies in physics, mathematics, statistics

and computer science curriculum. Students learn while they

play. Todd W. Neller et al. has used dice rolling in a dice game

Pig (Todd, Clifton, Ingrid, & Zdravko, 2006) for undergraduate

research in machine learning. Arthur Murray et al. mention that

“the ‘radioactive dice’ experiment is a commonly used class-

room analogue to model the decay of radioactive nuclei” (Ar-

thur & Ian, 2012). Simple dice rolling can unfold important

concepts elegantly.

Theory

Some radionuclides may have several different paths of de-

cay. For example, approximately 36% of Bismuth-212 decays

through alpha-emission to thallium-208 while approximately

64% of Bismuth-212 decays through beta-emission to Polo-

nium-212. Both the Thallium-208 and the Polonium-212 are

radioactive daughter products of Bismuth-212 and both decay

directly to stable Lead-208 (Tayal, 1988).

If a nucleus can decay by several different processes for

which the probabilities per unit time are λ1, λ2, λ3, ··· then the

total probability λ per unit time for decay is

123

and the half lives are related as

123

12 12 1212

11 11

TT TT

where

1

12

T is the half-life if only process 1 was available

and so on. These are called the partial half-lives. If one of them

is shorter than the others then it is dominant in determining

12

T.

Experiment

Dice Used

About 100 cuboctahedron (truncated cubes with 6 square

faces and eight triangular faces) have been used for the experi-

ments (Figure 1). In this experiment one of the six square faces

(suitably marked) and all of the triangular faces represent two

unstable states. The unmarked five square faces represent the

stable state of radioactive nuclei.

The dice represents a radioactive nucleus having many en-

ergy states. One of the states is represented by the yellow-

square-face. Eight of the triangular faces represent yet another

energy state. All the eight states have the same energy (degen-

erate states). Five of the unpainted square faces represent an-

other energy state.

Experimental Procedure

By rolling the dice a large number of times quantify the

probability per throw of yellow square face “up” (λ1) and any

red triangular face “up” (λ2). (In this experiment λ1 is smaller

than λ2.) Let the yellow square face “up” represent the alpha

decay and any red triangular face “up” represent the beta decay.

For each throw t (0, 1, 2, ···), start with Nt number of dice,

roll and remove the decayed nuclei (die with the specified face

“up”). Continue with the remaining un-decayed dice till about

ten percent of the dice is left. The entire process is repeated

once for alpha decay (Figure 2), once for beta decay (Figure 3)

and once for both the processes together (Figure 4).

Figure 1.

Truncated Cube (Cuboctahedron) with three types of

faces made from 3 cm wooden cubes.