Chapter 20, Problem 20.75QP

Interpretation Introduction

Interpretation: The age of the object should be determined by using the following data listed in question.

Concept Introduction:

• Half-life period: The time required to the reduce to half of its original value.
• This is denoted by: ${\text{t}}_{\text{1/2}}$
• This term is popularly use in nuclear chemistry, to describe the stability & unstability of atoms or radioactive decay.
• For determination of first order rate constant K in half –life period we use

  $\text{K=}\frac{\text{0}\text{.693}}{{\text{t}}_{\text{1/2}}}$ Equation.

• The half-life in first order does not depends upon the initial concentration.

Formula:

The number of disintegration is directly proportional to the number of radioactive nuclei

$\text{ln}\frac{\text{decay rate of old sample}}{\text{decay rate of fresh sample}}\text{=-kt}$

Age calculation:

$\text{ln}\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{0}}}\text{=-kt}$

Calculate the age and rate constant:

$\text{K=}\frac{\text{0}\text{.693}}{{\text{t}}_{\text{1/2}}}$

Given:

Carbon-14 decay rate of a sample =0.260dis/sec.

For another sample, its 0.186dis/sec

To find: Determine the rate constant by considering the age of carbon-14 isotope.