Chapter 20.3, Problem 1CP

Interpretation Introduction

Interpretation:

The age of the given rock sample is to be determined.

Concept Introduction:

The amount a particular radioactive isotope after time $t$ is given by the following expression:

$\text{ln}\frac{N_t}{N_o}\text{=}-\text{k}t$

Here, $\text{k}$ is the rate constant for the radioactive decay, $N_t$ is the amount of the sample left after time $t$, and $N_0$ is the initial amount of the sample.

Nearly all the radioactive decay is of first order and its rate constant is given as follows:

$\text{k = }\frac{0.693}{t_{1/2}}$

Here, $t_{1/2}$ is the half-life of the radioactive substance.