AQA · GCSE · Combined Science · Higher

Dice type and simulated half-life

Q06.3 2 marks

The number of times the dice have to be rolled to halve the original number of dice in the tray represents the half-life. Figure 7 shows an eight-sided dice and a six-sided dice. The student now used eight-sided dice to model radioactive decay. Dice that landed on the number six were again removed from the tray.

Photograph of an eight-sided dice and a six-sided dice, both showing numbered faces including 6. — Figure 7

The half-life represented by rolling eight-sided dice is likely to be different from the half-life represented by rolling six-sided dice. Explain how.

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Marking points

1 Explain that an eight-sided dice has a lower chance of landing on 6 in one roll than a six-sided dice.
2 Conclude that the eight-sided dice model has a greater half-life.

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An eight-sided dice has only a $1/8$ chance of landing on 6 in one roll, whereas a six-sided dice has a $1/6$ chance. Fewer dice are removed each roll with eight-sided dice, so it takes more rolls for the number of dice to halve. The eight-sided dice therefore represents a greater half-life.

Why this answer loses marks

The half-life is smaller because the dice has more sides.

More sides means the chance of rolling a 6 is smaller, so fewer dice decay each roll and the half-life is greater, not smaller.

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