Activity, half-life and the decay constant

Overview

Recall questions on activity and the becquerel, the decay constant, A = λN, half-life and T½ = ln2/λ, N = N₀e⁻λᵗ, calculating decay constants, activities and remaining fractions, the time to fall to one tenth, random decay giving a predictable pattern, why activity falls exponentially, and subtracting background.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Define the activity of a radioactive source and state its unit.

   Model answer

   Activity is the number of nuclei that decay per second in a sample, measured in becquerels, where one becquerel is one decay per second.

2. 2

   Define the decay constant.

   Model answer

   The decay constant λ is the probability per unit time that any individual nucleus will decay, and it is measured in s⁻¹.

3. 3

   Write the relationship between activity, decay constant and the number of undecayed nuclei.

   Model answer

   The activity is A = λN, where N is the number of nuclei that have not yet decayed.

4. 4

   Define the half-life of a radioactive isotope.

   Model answer

   The half-life is the average time taken for the number of undecayed nuclei in a sample, and therefore its activity, to fall to half its initial value.

5. 5

   Write the relationship between half-life and decay constant.

   Model answer

   The half-life is T½ = ln2/λ, so a large decay constant corresponds to a short half-life.

6. 6

   Write the equation giving the number of undecayed nuclei remaining after a time t.

   Model answer

   The number remaining is N = N₀e⁻λᵗ, where N₀ is the number present at the start.

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