Chapter 20, Problem 20.77QP

Interpretation Introduction

Interpretation: The percentage of radioactive C-14 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 ${\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}$
• This term is popularly use in nuclear chemistry, to describe the stability & instability of atoms or radioactive decay.
• For determination of first order rate constant K in half –life period we use

  $\text{K=}\frac{\text{0}\text{.629}}{{\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}}$ Equation.

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

Determine: the percentage and rate constant is being determine by considering the age of carbon-14 isotope.

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:

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

$\text{K=}\frac{\text{0}\text{.629}}{{\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}}$