Chapter 18, Problem 33QAP

Interpretation Introduction

(a)

Interpretation:

The time required to decrease the activity 30 % of its original value needs to be determined.

Concept introduction:

All the radioactive reactions are first order reactions. For first order reaction, the relation between rate constant, k and half-life time is as follows:

$k=\frac{0.6932}{t_{1/2}}$

Also, the integrated rate expression can be written as follows:

$t=\frac{2.303}{k}\log \frac{A_o}{A_t}$

Here, t is time required to decrease the amount of substance from $A_o$ to $A_t$ and k is rate constant for the reaction.

Interpretation Introduction

(b)

Interpretation:

The percent of original activity remaining after 10 years needs to be determined.

Concept introduction:

All the radioactive reactions are first order reactions. For first order reaction, the relation between rate constant, k and half-life time is as follows:

$k=\frac{0.6932}{t_{1/2}}$

Also, the integrated rate expression can be written as follows:

$t=\frac{2.303}{k}\log \frac{A_o}{A_t}$

Here, t is time required to decrease the amount of substance from $A_o$ to $A_t$ and k is rate constant for the reaction.