Chapter 20, Problem 80AP

Interpretation Introduction

Interpretation:

The balanced equation for the reaction of the radioactive decay of potassium $40$ isotope to argon $40$ is to be represented and the age of the rock sample is to be determined.

Concept Introduction:

The amount of a particular radioactive isotope left, after time t, is given as

$\text{ln}\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{o}}}\text{=}-kt$

Here, $k$ is the rate constant for the radioactive decay, ${\text{N}}_{\text{t}}$ is the amount of it left after time t, and ${\text{N}}_{\text{0}}$ is the initial amount of the sample.

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

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

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

In a balanced radioactive decay,

${\displaystyle \sum \text{Reactant mass number = }{\displaystyle \sum \text{Product mass number}}}$

${\displaystyle \sum \text{Reactant atomic number = }{\displaystyle \sum \text{Product atomic number}}}$