Chapter 20, Problem 20.94QP

(a)

Interpretation Introduction

Interpretation:

Suitable assumption should be drawn for the given calculation.

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

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

The activity is given by:

$\text{activity=}\frac{\text{numberdecay}}{\text{Unit time}}\text{=kN}$

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 half-life of ${\text{Mg}}^{\text{27}}$ is 9.50 min.

Initially 4.20 ${\text{×10}}^{12}\text{years}$ ${\text{Mg}}^{\text{27}}$ nuclei present.

To determine: Determine the remaining ${\text{Mg}}^{\text{27}}$ nuclei after 30.00 min

(b)

Interpretation Introduction

Interpretation:

Suitable assumption should be drawn for the given calculation.

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

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

The activity is given by:

$\text{activity=}\frac{\text{numberdecay}}{\text{Unit time}}\text{=kN}$

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 half-life of ${\text{Mg}}^{\text{27}}$ is 9.50 min.

Initially 4.20 ${\text{×10}}^{12}\text{years}$ ${\text{Mg}}^{\text{27}}$ nuclei present.

To determine: The ${\text{Mg}}^{\text{27}}$ activity (in Ci) at t=0 and t=30.0min is calculated.

(c)

Interpretation Introduction

Interpretation:

Suitable assumption should be drawn for the given calculation.

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

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

The activity is given by:

$\text{activity=}\frac{\text{numberdecay}}{\text{Unit time}}\text{=kN}$

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 half-life of ${\text{Mg}}^{\text{27}}$ is 9.50 min.

Initially 4.20 ${\text{×10}}^{12}\text{years}$ ${\text{Mg}}^{\text{27}}$ nuclei present.

To determine: Probability of finding ${\text{Mg}}^{\text{27}}$ nuclei decay during a 1 s interval