Chapter 19, Problem 24A

Interpretation Introduction

Interpretation: The given radioactive nuclides in the mentioned table needs to be arranged in order of relative decay activities.

Concept introduction:

For a radioactive nuclide, the half-life is defined as time required to take a nucleus sample to become half of its initial value. If the initial amount is A, the amount left after half-life will be A/2.

The decay activity is inversely proportional to the half-life.

Explanation of Solution

The radioactive nuclides and their half-lives are as follows:

Radioactive nuclide	Half-life
${}^{87}\text{Sr}$	2.8 hours
${}^{99}\text{Tc}$	6.0 hours
${}^{24}\text{Na}$	14.8 hours
${}^{99}\text{Mo}$	67 hours
${}^{133}\text{Xe}$	5.3 days
${}^{131}\text{I}$	8.1 days
${}^{32}\text{P}$	14.3 days
${}^{87}\text{Sr}$	27.8 days
${}^{59}\text{Fe}$	45.1 days

Thus, the relative order of the decay activities will be decreasing order of the half-life time or it can be said that as half-life increases, decay activity decreases.

The decreasing order of the decay activity will be as follows:

  ${}^{87}{\text{Sr>}}^{99}\text{Tc}{>}^{24}\text{Na}{>}^{99}\text{Mo}{>}^{133}\text{Xe}{>}^{131}\text{I}{>}^{32}\text{P}{>}^{87}{\text{Sr>}}^{59}\text{Fe}$