Chapter 19, Problem 19.95SP

Interpretation Introduction

Interpretation:

The decay equation can therefore be written:

$N_t=N_o{e}^{-\lambda t}$

Concept introduction:

Since $Ar$ was also formed from $K$

  $K{}_0=K{}_t+A{r}_t$

Where  $A{r}_t$ is the number of $Ar$ atoms formed after time t.
The decay equation can therefore be written:

  $N_t=N_o{e}^{-\lambda t}$

Given:

$K{}_{}\stackrel{}{\to }Ar+e{}_{}$

Half-life of $K$ = $1.25\times {10}^9$ years
$K$ decays to give $Ar$

Concentration of $K$ in the rock = $3.35mmol$

Concentration of $Ar$ in the rock = $0.25mmol$

To determine:

The time taken by the rock to cool