Chapter 14, Problem 14.90PAE

Interpretation Introduction

Interpretation:

The sample of ⁷⁰Ga with a half0life of 21.1 minutes produces 455 counts per second. The time at which the sample of ⁷⁰Ga would produce 115 counts per second should be calculated.

Concept Introduction:

All radioactive reactions follow first-order kinetics.

For a first order reaction, rate constant and half-life time are related to each other as follows:

$k=\frac{0.693}{t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$

Here,

$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ is half-life time

k is the decay constant of the reaction

First order rate equation is as follows:

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

Here,

t is the time-period

$A_t$ is concentration of the nuclei at time t

$A_o$ is the initial concentration of the nuclei