Throwing large numbers of dice can be used to model radioactive decay.
An experiment is conducted using 500500500 eight-sided (octahedral) dice, each with one face painted red. All 500500500 dice are rolled. Any dice that land with the red face uppermost are removed, representing nuclei that have "decayed". The remaining dice are gathered and rolled again, and the process is repeated.
The table below shows the number of dice remaining after each of the first 888 throws:
Throw (t)012345678Dice remaining (N)500435380331288254221192169\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \text{Throw } (t) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Dice remaining } (N) & 500 & 435 & 380 & 331 & 288 & 254 & 221 & 192 & 169 \\ \hline \end{array}Throw (t)Dice remaining (N)050014352380333142885254622171928169Complete the following sentence:
The half-life of a radioactive isotope is the time taken for the number of radioactive nuclei in a sample to decrease to .................... of its initial value.
Using the data in the table:
Determine the target number of remaining dice corresponding to one "half-life" of the dice.
Using the data in the table:
Estimate the "half-life" (in number of throws) of these dice from the table. Explain your reasoning.
The experiment is repeated, but this time starting with 120012001200 of the same eight-sided dice.
Suggest how many throws it would take to reduce the number of remaining dice to 600600600.
The experiment is repeated, but this time starting with 120012001200 of the same eight-sided dice.
Explain your answer.
484 exam-style questions on CIE IGCSE Physics 5.2 Radioactivity, covering 5.2.1 Background radiation and measuring count rate, 5.2.2a Alpha, beta and gamma emission, 5.2.2b Deflection and ionising effects of nuclear radiation, 5.2.3a Radioactive decay, 5.2.3b Effects of decay on the nucleus and decay equations, 5.2.4a Half-life, 5.2.4b Choosing isotopes for applications, and 5.2.5 Effects of ionising radiation and safety precautions. Each one has a worked solution and a mark scheme showing where the marks go.