Chapter 19, Problem 19.55QP

Interpretation Introduction

Interpretation:

The unit, curie has to be derived for which half-life of ${}_{88}^{226}Ra$ is $1.6\times {10}^{3}yr$

Concept Introduction:

• The rate of radioactive decay at any time $t$ is given by

$Rateofdecayattimet=\lambda N$, where $\lambda$ is the first-order rate constant and $N$ is the number of radioactive nuclei present at any time $t$.

• Number of radioactive nuclei at time zero $\left(N_0\right)$ and time $t$$\left(N_t\right)$ is given by

$\ln \frac{N_t}{N_0}=-\lambda t$

• Half-life of the reaction is given by

$t_{1/2}=\frac{0.693}{\lambda }$