24.31 P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: After 1 minute, three radioactive nuclei remain from an original sample of six. Is it valid to conclude that ${\mathit{t}}_{\mathbf{1}\mathbf{/}\mathbf{2}}$ equals 1 minute? Is this conclusion valid if the original sample contained $\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}$ nuclei and $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}$ remain after 1 minute? Explain.

Step-by-Step Solution

Answer

It is not true that after 1 minute, three radioactive nuclei remain from an original sample of six.

Step 1: Activity of radio isotope

The decrease in the number of radioactive nuclei per unit time is the rate of decay, or activity, of a sample of a radioactive substance.

Step 2: Explanation

The decay rate is an average rate that is only relevant when the sample is macroscopic and has a significant number of nuclei.

Because the number of nuclei in the issue is so little, it is not valid to conclude that ${\text{t}}^{\frac{1}{2}}$ equals 1min. It isn't true.