5 The number of radioactive atoms, \(N\), in a sample of a sodium isotope after time \(t\) hours can be modelled by
$$N = N _ { 0 } \mathrm { e } ^ { - k t }$$
where \(N _ { 0 }\) is the initial number of radioactive atoms in the sample and \(k\) is a positive constant.
The model remains valid for large numbers of atoms.
5
- It takes 15.9 hours for half of the sodium atoms to decay.
Determine the number of days required for at least \(90 \%\) of the number of atoms in the original sample to decay.
[0pt]
[5 marks]
5 - Find the percentage of the atoms remaining after the first week.
Give your answer to two significant figures.
5 - Explain why the model can only provide an estimate for the number of remaining atoms.
5 - Explain why the model is invalid in the long run.