Chapter 19.3, Problem 1RCF

Interpretation Introduction

Interpretation:

Mass of ${}_{19}^{42}K$ remaining after 100hours if the original sample had 256g has to be identified.

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

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