Chapter 9, Problem 9.47AP

(a)

Interpretation Introduction

Interpretation:

The amount of Iodine-131and Xenon-131 remains after $\text{8}\text{d}$ has to be given.

Answer to Problem 9.47AP

The amount of Iodine-131 remains after $\text{8}\text{d}$ is $\text{32}\text{mg}\text{.}$

The amount of Xenon-131 remains after $\text{8}\text{d}$ is $\text{32}\text{mg}\text{.}$

Explanation of Solution

Given,

The mass of Iodine-131 at initial is $\text{64}\text{mg}\text{.}$

The half-life of Iodine-131 is $\text{8}\text{d}\text{.}$

The time interval is $\text{8}\text{d}\text{.}$

The number of days can be converted to the number of half life by,

  $\text{8}\text{d×}\frac{\text{1}\text{half}\text{life}}{\text{8}\text{d}}\text{=1}\text{Half}\text{Life}$

The amount of substance remains after half lives can be calculated by multiplying half lives with the initial mass,

The amount of substance remains after one half-lives (m) $\text{=64}\text{mg×}\frac{\text{1}}{\text{2}}$

  $\text{m=}\frac{64\text{mg}}{2}$

  $\text{m=}32\text{mg}$

The amount of Iodine-131 remains after $\text{8}\text{d}$ is $\text{32}\text{mg}\text{.}$

The amount of Xenon-131 after $\text{8}\text{d}$ can be calculated as,

The amount of Xenon-131=$\left(\text{Total}\text{mass-Mass}\text{of}\text{iodine}\right)$

The amount of Xenon-131=$\left(\text{64-32mg}\right)$

The amount of Xenon-131=$\text{32}\text{mg}$

The amount of Xenon-131 remains after $\text{8}\text{d}$ is $\text{32}\text{mg}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The amount of Iodine-131 and Xenon-131 remains after $16\text{d}$ has to be given.

Answer to Problem 9.47AP

The amount of Iodine-131 remains after $16\text{d}$ is $16\text{mg}\text{.}$

The amount of Xenon-131 remains after $16\text{d}$ is $48\text{mg}\text{.}$

Explanation of Solution

Given,

The mass of Iodine-131 at initial is $\text{64}\text{mg}\text{.}$

The half-life of Iodine-131 is $\text{8}\text{d}\text{.}$

The time interval is $16\text{d}\text{.}$

The number of days can be converted to the number of half life by,

  $16\text{d×}\frac{\text{1}\text{half}\text{life}}{\text{8}\text{d}}\text{=2}\text{Half}\text{Life}$

The amount of substance remains after half lives can be calculated by multiplying half lives with the initial mass,

The amount of substance remains after two half-lives (m) $\text{=64}\text{mg×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}$

  $\text{m=}\frac{\text{64}\text{mg}}{\text{4}}$

  $\text{m=}16\text{mg}$

The amount of Iodine-131 remains after $16\text{d}$ is $16\text{mg}\text{.}$

The amount of Xenon-131 after $16\text{d}$ can be calculated as,

The amount of Xenon-131=$\left(\text{Total}\text{mass-Mass}\text{of}\text{iodine}\right)$

The amount of Xenon-131=$\left(\text{64-16g}\right)$

The amount of Xenon-131=$\text{48}\text{mg}$

The amount of Xenon-131 remains after $16\text{d}$ is $48\text{mg}\text{.}$

(c)

Interpretation Introduction

Interpretation:

The amount of Iodine-131 and Xenon-131 remains after $\text{24}\text{d}$ has to be given.

Answer to Problem 9.47AP

The amount of Iodine-131 remains after $\text{24}\text{d}$ is $\text{8}\text{mg}\text{.}$

The amount of Xenon-131 remains after $\text{24}\text{d}$ is $56\text{mg}\text{.}$

Explanation of Solution

Given,

The mass of Iodine-131 at initial is $\text{64}\text{mg}\text{.}$

The half-life of Iodine-131 is $\text{8}\text{d}\text{.}$

The time interval is $\text{24}\text{d}\text{.}$

The number of days can be converted to the number of half life by,

  $\text{24}\text{d×}\frac{\text{1}\text{half}\text{life}}{\text{8}\text{d}}\text{=3}\text{Half}\text{Life}$

The amount of substance remains after half lives can be calculated by multiplying half lives with the initial mass,

The amount of substance remains after three half-lives (m) $\text{=64}\text{mg×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}$

  $\text{m=}\frac{\text{64}\text{mg}}{\text{8}}$

  $\text{m=}8\text{mg}$

The amount of Iodine-131 remains after $\text{24}\text{d}$ is $\text{8}\text{mg}\text{.}$

The amount of Xenon-131 after $\text{24}\text{d}$ can be calculated as,

The amount of Xenon-131=$\left(\text{Total}\text{mass-Mass}\text{of}\text{iodine}\right)$

The amount of Xenon-131=$\left(\text{64-8}\text{mg}\right)$

The amount of Xenon-131=$\text{56}\text{mg}$

The amount of Xenon-131 remains after $\text{24}\text{d}$ is $56\text{mg}\text{.}$

(d)

Interpretation Introduction

Interpretation:

The amount of Iodine-131 and Xenon-131 remains after $32\text{d}$ has to be given.

Answer to Problem 9.47AP

The amount of Iodine-131 remains after $32\text{d}$ is $4\text{mg}\text{.}$

The amount of Xenon-131 remains after $32\text{d}$ is $60\text{mg}\text{.}$

Explanation of Solution

Given,

The mass of Iodine-131 at initial is $\text{64}\text{mg}\text{.}$

The half-life of Iodine-131 is $\text{8}\text{d}\text{.}$

The time interval is $32\text{d}$

The number of days can be converted to the number of half life by,

  $\text{32}\text{d×}\frac{\text{1}\text{half}\text{life}}{\text{8}\text{d}}\text{=4}\text{Half}\text{Life}$

The amount of substance remains after half lives can be calculated by multiplying half lives with the initial mass,

The amount of substance remains after four half-lives (m) $\text{=64}\text{mg×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}\text{×}\frac{\text{1}}{\text{2}}$

  $\text{m=}\frac{\text{64}\text{mg}}{\text{16}}$

  $\text{m=}4\text{mg}$

The amount of Iodine-131 remains after $32\text{d}$ is $4\text{mg}\text{.}$

The amount of Xenon-131 after $32\text{d}$ can be calculated as,

The amount of Xenon-131=$\left(\text{Total}\text{mass-Mass}\text{of}\text{iodine}\right)$

The amount of Xenon-131=$\left(\text{64-4}\text{mg}\right)$

The amount of Xenon-131=$\text{60}\text{mg}$

The amount of Xenon-131 remains after $32\text{d}$ is $60\text{mg}\text{.}$