Chapter 20, Problem 20.81QP

Interpretation Introduction

Interpretation: Avogadro’s number should be calculated by using the definition of curie.

Concept Introduction:

• Half-life period: The time required to reduce the 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 & instability of atoms or radioactive decay.
• For determination of first order rate constant K in half –life period we use

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

Definition:

1 curie corresponds to exactly 3.7 ${\text{×10}}^{\text{10}}\text{nuclear dis/sec}$

This is the decay rate equivalent to that of 1 g of radium.

Thus the mass of 2.70 ${\text{×10}}^{\text{21}}\text{Ra}$ atoms is 1 g.

Formula:

• The rate of decay of the isotope is given by the rate law:

Rate=KN

• 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: the molar mass of ${}^{226}\text{Ra}$is 226.03g/mol.

Half-life decay 1.6 ${\text{×10}}^{\text{3}}\text{years}$.

To identify: Avogadro’s number is calculated by using the definition of curie.