AQA GCSE Combined Science: Trilogy Physics Paper 1 (Higher), 2020: Question 6

7 marks · Standard Demand difficulty · Short Answer

Explain and calculate aspects of radioactive decay and half-life using a dice model, including comparing decay probabilities and nuclear stability.

Practise this question

Question

The question page contains four linked parts about modelling radioactive decay with dice. Part 06.1 asks why rolling dice is a suitable model for radioactive decay after stating that dice landing on six are removed and represent decayed nuclei; part 06.2 says 144 dice were rolled repeatedly, with sixes removed each time, and after 20 rolls 9 dice remained, then asks for the most likely number of rolls before the number halved, showing working. Part 06.3 defines half-life in this model and shows Figure 7, a photo of an eight-sided die beside a six-sided die, then asks how using eight-sided dice with sixes removed would change the half-life. Part 06.4 states source A has a longer half-life than source B and asks what can be deduced about the nuclei in A compared with B, without referring to isotopes.
Question text

06 A student modelled radioactive decay by rolling some dice in a tray.

Dice that landed on the number six were removed from the tray.

The removed dice represent nuclei that have decayed.

06.1 Why is rolling dice a suitable model for radioactive decay?

[1 mark]

06.2 The student rolled 144 dice and removed all those that landed on the number six.

The student rolled the remaining dice and again removed all those that landed on the

number six.

When the student had rolled the dice 20 times there were 9 dice left.

Calculate the most likely number of times that the student had rolled the dice before

the number of dice had halved.

You should show how you work out your answer.

[3 marks]

Answer =21 rolls of the dice

06.3 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.

Figure 7

The student now used eight-sided dice to model radioactive decay. Dice that landed

on the number six were again removed from the tray.

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.

[2 marks]

06.4 A teacher has two radioactive sources, A and B.

Source A has a longer half-life than source B.

What can be deduced about the nuclei in source A compared with the nuclei

in source B?

Do not refer to isotopes in your answer.

[1 mark]

Mark scheme

Show the mark scheme The mark scheme is a table with columns for Question, Answers, Extra information, Mark, and AO/Spec Ref. For 06.1 it awards 1 mark for stating both rolling dice and radioactive decay are random processes; for 06.2 it gives marks for showing the halving sequence 144 to 72 to 36 to 18 to 9, identifying 4 half-lives, and calculating 20 divided by 4 equals 5 rolls, with alternatives using probability 5/6 and 144 × (5/6)^4 = 69 accepted. For 06.3 it awards marks for saying an 8-sided die has a smaller chance of decay in one roll, such as 1/8 instead of 1/6, so the half-life is greater; for 06.4 it awards 1 mark for stating nuclei in source A are more stable or less likely to decay in a given time period than those in source B.

AO /

Question Answers Extra information Mark

Spec. Ref.

06.1 both are random processes allow rolling dice is a random 1 AO1

process 6.4.2.3

allow radioactive decay is a

random process

06.2 144 →72 → 36 →18 → 9 allow the probability of not 1 AO2

getting a 6 is 5/6 6.4.2.3

4 half lives allow 144 × (5/6) = 69

20 allow 69 is closest to 72 so 4 1

= 5 (rolls of the dice)

4 (rolls of the dice)

some credible working must be

shown to gain this mark

06.3 a dice with 8 sides will have a allow answers in terms of the 6- 1 AO1

smaller chance of decay (in one sided dice or in terms of more or 6.4.2.3

roll) fewer sides.

allow the 8 sided dice has a 1/8

chance of decay, whereas the 6

sided dice has a 1/6 chance of

decay

so dice with 8 sides have a 1

greater half-life

06.4 nuclei in source A are more allow nuclei in source A are less 1 AO1

stable than nuclei in source B likely to decay (in a given time 6.4.2.3

period)

Total 7

How to answer it

Radioactive Decay Dice Model

What this question tests
This question checks your understanding of the random nature of radioactive decay, how to use a dice model to estimate half-life, and how changing the probability of decay changes the half-life. You also need to explain a simple idea clearly for 1-mark answers and show working neatly for the calculation.
Question 06 overview

Dice as a model for radioactive decay

💡 Key knowledge

  • Radioactive decay is random.
  • In the model, each die roll represents a chance of a nucleus decaying.
  • A result of 6 means that “nucleus” is removed.
  • Half-life is the time/number of rolls needed for half the nuclei to decay.

🧠 Exam technique

  • Use the exact wording in the question: random process, half-life, more stable.
  • For 1 mark, one clear correct statement is enough.
  • For calculations, show a chain of halving if possible — examiners award credit for sensible working.

❌ Common errors

  • Saying the dice model is “accurate” instead of explaining why it is suitable.
  • Forgetting that decay is random.
  • Confusing half-life with “one roll” or “number of dice removed”.
  • Not showing working in part (b), which can lose the method mark.

Part (a) 06.1 Why is rolling dice a suitable model for radioactive decay?

✅ Correct answer

Both are random processes.

💡 Key knowledge

Radioactive decay happens unpredictably. You cannot tell exactly which nucleus will decay next, just like you cannot predict exactly which die will land on a 6.

🧠 Exam technique

For a 1-mark question, keep it short. A phrase like “both are random” is enough. You do not need a long explanation.

❌ Common errors

Do not say “because they both change over time” or “because they are both unpredictable” without linking to randomness. The mark scheme wants the idea of a random process.

Part (b) 06.2 Calculate the most likely number of rolls before the number of dice had halved

📐 Calculations: step-by-step

  1. Start with 144 dice.
  2. Each roll removes about 1/6, so about 5/6 remain each time.
  3. Halving sequence:
    144 → 72 → 36 → 18 → 9
  4. It takes 4 half-lives to go from 144 to 9.
  5. The dice were rolled 20 times in total, so:
    20 ÷ 4 = 5
  6. Answer = 5 rolls of the dice

✅ Correct answer

5 rolls

Marking idea: 1 mark for getting the halving chain, 1 mark for identifying 4 half-lives, 1 mark for dividing 20 by 4 to get 5.

💡 Key knowledge

  • Half-life means the amount halves each time.
  • Starting with 144, four halvings gives 9.
  • Since 20 rolls corresponds to 4 half-lives, one half-life is 5 rolls.

❌ Common errors and traps

  • Using 72 as the final answer — that is only half once.
  • Dividing 144 by 20 — this is not what the question asks.
  • Forgetting to show the halving sequence, which can cost the method mark.
  • Writing 20 ÷ 5 = 4 backwards.

🧠 How to score full marks

A top answer usually includes:

  • A correct halving pattern: 144 → 72 → 36 → 18 → 9
  • The statement 4 half-lives
  • The final division 20 ÷ 4 = 5

Part (c) 06.3 Explain why eight-sided dice give a different half-life from six-sided dice

✅ Correct answer

A dice with 8 sides will have a smaller chance of decay in one roll, so it will have a greater half-life.

💡 Key knowledge

  • With 6 sides, the chance of decay is 1/6.
  • With 8 sides, the chance of decay is 1/8.
  • A smaller chance of decay means it takes longer for half the dice to be removed.

🧠 Exam technique

  • To get both marks, link probability to half-life.
  • Use comparison words: smaller chance, greater half-life.
  • You can mention the numbers: 1/8 and 1/6.

❌ Common errors

  • Saying 8-sided dice have a greater chance of decay — this is backwards.
  • Saying “the half-life is the same” because both are random. Random does not mean identical probability.
  • Not linking to half-life at all.

Part (d) 06.4 What can be deduced about the nuclei in source A compared with source B?

✅ Correct answer

Nuclei in source A are more stable than nuclei in source B.

💡 Key knowledge

A longer half-life means nuclei are less likely to decay in a given time. That means they are more stable.

🧠 Exam technique

Use the wording from the mark scheme: more stable is the safest answer. If you want, you can also say they are less likely to decay in a given time period.

❌ Common errors

  • Saying source A is “more radioactive” — that would usually mean less stable.
  • Referring to isotopes when the question says do not refer to isotopes.
  • Writing only “A has a longer half-life” without explaining what that means about the nuclei.

🧠 Examiner insight: what distinguishes full marks

Top answers are short but precise. They make the link:

longer half-life → slower decay → more stable nuclei

That is exactly the kind of causal chain examiners reward.

Quick revision summary

💡 Remember

  • Random decay can be modelled by random die rolls.
  • Each 6 represents a decay event.
  • Half-life is the number of rolls needed to halve the number remaining.
  • More sides on the die = lower chance of decay per roll = longer half-life.
  • Longer half-life = nuclei are more stable.

🧠 Last exam tip

When a question says “explain”, give the reason and the conclusion. When it says “calculate”, show the steps clearly and include the final unit or label where needed.

Topics

Physics · P4: Atomic Structure

Question and mark scheme from the AQA GCSE Combined Science: Trilogy examination, Physics Paper 1 (Higher), 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.