A student models radioactive decay using 600 dice. Each die is a small cube of wood with one face painted red. The 600 dice are thrown. All dice that land with the red face uppermost are removed (they are considered to have "decayed"). The remaining dice are thrown again, and those landing with the red face uppermost are again removed. This process is repeated.
The table below shows the number of dice remaining after each throw:
| Throw | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Number of dice remaining | 600 | 504 | 412 | 348 | 292 | 238 | 202 | 165 | 140 |
Complete the sentence: The half-life of a radioactive isotope is the time taken for the number of nuclei in a sample to decrease to ............................... of its initial value.
Throwing dice obeys the same statistical laws as radioactive decay. (i) Calculate the number of dice remaining when the initial quantity of dice has halved.
(ii) Using the data in the table, estimate the "half-life" of these dice in terms of the number of throws.
The experiment is repeated, starting this time with 1600 dice. (i) State how many throws it will take to reduce the number of dice to 800.
(ii) Explain your answer in terms of the properties of radioactive decay.
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.