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Cambridge International AS & A Level · 23 · structured

Spontaneous decay, decay constant and activity

Spontaneous decay, decay constant and activity · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
6
Topics
2
Answer
Complete
structured6 marks

A radioactive sample contains 3.00×10¹² undecayed nuclei and has decay constant λ=2.00×10⁻⁵ s⁻¹ at the instant considered.

  1. (a)

    Distinguish the statements that radioactive decay is spontaneous and that it is random.

    2 marks
  2. (b)

    Define activity and decay constant, give their units and calculate the sample activity.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overview(a) Spontaneous: no external trigger is required. Random: the decay time of an individual nucleus cannot be predicted. (b) Activity is decay rate in Bq=s⁻¹; λ is probability per unit time for one undecayed nucleus, s⁻¹; A=λN=6.00×10⁷ Bq.
01

(a)

2 marks

Distinguish the statements that radioactive decay is spontaneous and that it is random.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    Spontaneous decay occurs without requiring an external event to initiate each decay.

  2. 2

    Random means one cannot predict exactly which nucleus will decay or when, although ensemble probabilities can be specified.

02

(b)

4 marks

Define activity and decay constant, give their units and calculate the sample activity.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    Activity is the number of nuclear decays per unit time; its SI unit is Bq, equivalent to s⁻¹.

  2. 2

    The decay constant is the decay probability per unit time for a single undecayed nucleus; unit s⁻¹.

  3. 3

    Use A=λN.

  4. 4

    A=2.00×10⁻⁵×3.00×10¹²=6.00×10⁷ Bq; this is the total decay rate, not automatically a detector's count rate.

Complete marking guidance

Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.

  1. (a) Spontaneous decay occurs without requiring an external event to initiate each decay.
  2. (a) Random means one cannot predict exactly which nucleus will decay or when, although ensemble probabilities can be specified.
  3. (b) Activity is the number of nuclear decays per unit time; its SI unit is Bq, equivalent to s⁻¹.
  4. (b) The decay constant is the decay probability per unit time for a single undecayed nucleus; unit s⁻¹.
  5. (b) Use A=λN.
  6. (b) A=2.00×10⁻⁵×3.00×10¹²=6.00×10⁷ Bq; this is the total decay rate, not automatically a detector's count rate.

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Your self-assessment

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