The exponential decay law in calculations

Overview

Recall questions on The exponential decay law in calculations.

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

   State the exponential decay law for the number of undecayed nuclei, defining each symbol.

   Model answer

   N = N₀e^(−λt), where N is the number of undecayed nuclei remaining after time t, N₀ the number present at t = 0 and λ the decay constant in s⁻¹.

2. 2

   State the exponential decay law written in terms of activity.

   Model answer

   A = A₀e^(−λt), where A is the activity after time t and A₀ the initial activity, both in Bq.

3. 3

   State the form of the decay law that uses the number of half-lives elapsed.

   Model answer

   N = N₀/2ˣ, and equally A = A₀/2ˣ, where x is the number of half-lives that have elapsed.

4. 4

   Must the number of half-lives x be a whole number?

   Model answer

   No. x is simply the elapsed time divided by the half-life and can take any positive value, whole or fractional.

5. 5

   Describe the shape of a graph of the number of undecayed nuclei against time.

   Model answer

   It is a curve that falls steeply at first and then flattens out, approaching the time axis without ever reaching it. Equal intervals of time always produce the same fractional decrease.

6. 6

   How can the exponential decay law be turned into a straight-line graph, and what do the gradient and intercept give?

   Model answer

   Taking natural logarithms of A = A₀e^(−λt) gives ln A = ln A₀ − λt, so plotting ln A against t gives a straight line. The gradient is −λ and the intercept on the vertical axis is ln A₀.

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