Chapter 19, Problem 21A

Interpretation Introduction

Interpretation: The half life of radioactive nucleus needs to be defined. Whether the given type nucleus have always same half life or not needs to be determined. Whether a nuclei of different element have same half life or not needs to be determined.

Concept introduction: During radioactive decay, instantaneous conversion of all atoms of one element into atoms of another element does not occur but the decay process takes time.

The half-life of a nucleus can be defined as the time taken for one-half of the original sample of nuclei to decay.

Half life can be calculated from the decay constant of the radionuclide. The relationship between them is,

  $\begin{array}{l}{t}_{1/2}=\frac{\text{ln2}}{\lambda }\text{ where, }{t}_{1/2}=\text{ half life of the radionuclide}\\ \lambda \text{= decay constant of the process}\end{array}$

Answer to Problem 21A

Given type of nucleus has always same half life. Different types of nucleus have always different half life.

Explanation of Solution

A given isotope of an element always has the same half-life but if isotope is changed then the half life will be changed. Nucleus changes when we go from one isotope to another. For example half life of two isotopes of phosphorous $P$ and $P$ are 14 days and 25 days respectively.

For nuclei of different element value of decay constant will differ. Since half life is inversely proportional to decay constant it will change with change of the nuclei. For example half life of $Li$ and $Na$ are 24 hour and 15 hour respectively.

Conclusion

Given type of nucleus has always same half life. Different types of nucleus have always different half life.