Model of radioactive decay using dice

Frontline

Radioactivity

Model of radioactive decay using dice Dice rolling is a useful pedagogical tool to introduce students to the concepts and essential features of radioactivity. It can be extended to simulate successive radioactive decay and thus explain half-life, decay constant, activity, different generations (parent, daughter nuclei), change of activity of parent and daughter nuclei with time and the behaviour of parent and daughter activiMay 2011

ties in special situations including ‘radioactive equilibrium’. Students also learn about stastistical fluctuations. The simulations that are described below can either be done by students or demonstrated by a teacher. The relevant background theory, my own data from the simulations and corresponding Excel graphs can be obtained at stacks.iop.org/ P h ysic s E ducat ion

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Frontline Table 1. Combinations for parent decay and daughter decay Simulation

Probability of parent decay

Probability of daughter decay

1 p1 p3 2 p1 p2 3 p1 p1 4 p2 p1 5 p3 p1

Remarks Significantly long-lived parent Relatively long-lived parent Almost equal half-life of parent and daughter Relatively short-lived parent Significantly short-lived parent

physed/46/255/mmedia. Make up 100 cuboctahedra (truncated cubes with six square faces and eight triangular faces; figure 1). One of the six square faces (suitably marked) and all of the triangular faces represent two unstable states. The rest of the square faces represent the third unstable state. Roll the die a large number of times to determine the probabilities per throw for the marked square face ‘up’ (p1), any triangular face ‘up’ (p2) and unmarked square face up (p3). With faces marked as above, p1 is smaller than p2, and p3 is significantly (several times) higher than p1 and p2. The same die is used for both parent and daughter, but with different type of face ‘up’ as the unstable Figure 1. Cuboctahedron (truncated cube) with state. Using these cuboctahedra, you can simulate dif- three types of faces. ferent combinations for parent decay and daughter decay (table 1). ●● When parent nuclei are relatively short-lived compared with daughter nuclei (λp > λd), no Typical results equilibrium is attained. My data show that p1 = 0.13 ± 0.03, p2 = 0.18 ± 0.05 ●● Very short-lived parent nuclei (λp & λd) get and p3 = 0.67 ± 0.08. converted to daughter nuclei in a relatively Let λp and λd be the decay constants for parent short time. The ratio of daughter activity to and daughter nuclei. Excel graphs from the simulaparent activity increases continuously with tions show the following: time. ●● In the case of significantly long-lived parent nuclei (λp « λd), daughter nuclei achieve secular Acknowledgements equilibrium after a time significantly higher My sincere thanks to my husband, R P Sahu, for than the daughter half-life. his guidance and support in using Microsoft Excel ●● For relatively long-lived parent nuclei (λp < λd), for the tabulations and graph. Thanks also to the the daughter achieves transient equilibrium and referee for valuable suggestions in improving the the parent–daughter activity ratio lies between text. 0 and 1 during transient equilibrium. ●● When parent and daughter nuclei have almost Sarmistha Sahu Head of Physics Department, equal half-lives (λp b λd), the parent–daughter Maharani Lakshmi Ammanni College for activity ratio increases linearly with time. Women, Science Post, Bangalore 560012, India 256

P h ysic s E ducat ion

May 2011