Chapter 21, Problem 21.63QP

(a)

Interpretation Introduction

Interpretation:

The radius (r) of a nucleus is directly proportional to the (${\text{r}}^{\text{3}}$) of mass number (A) to be shown and the volume for ${\text{U}}_{}^{\text{235}}$ nucleus should be determined.

Concept Introduction:

• Half-life period: The time required to reduce 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.

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

Formula:

The volume of a sphere is $\text{V=}\frac{\text{4}}{\text{3}}{\text{πr}}^{\text{3}}$

Age calculation:

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

Calculate the age and rate constant:

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

(b)

Interpretation Introduction

Interpretation:

The radius (r) of a nucleus is directly proportional to the (${\text{r}}^{\text{3}}$) of mass number (A) to be shown and the volume for ${\text{U}}_{}^{\text{235}}$ nucleus should be determined.

Concept Introduction:

• Half-life period: The time required to reduce 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.

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

Formula:

The volume of a sphere is $\text{V=}\frac{\text{4}}{\text{3}}{\text{πr}}^{\text{3}}$

Age calculation:

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

Calculate the age and rate constant:

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

To determine: The calculated volume for the ${\text{U}}_{}^{\text{235}}$ nucleus by substituting the equation derived in step-1.