Chapter 6, Problem 6C.9E

(a)

Interpretation Introduction

Interpretation:

How much ${}^{90}Sr$ will remain after the half-life of 19 a if none is lost metabolically has to be found.

Concept introduction:

Half-life: The time taken for one-half of the nuclei in the sample to decay.  The half-life of the sample is independent of the quantity of radioactive material and depends on the decay constant of the nuclide in the sample.

The decay constant (k) is independent of the quantity of radioactive material however depends only on the character of the nuclide.  Various nuclides have various decay constants.  The degree of radioactive decay depends on the decay constant and number of radioactive nuclei at specific time (${\text{N}}_{\text{t}}$).  The rate of decay is directly proportional to the number of radioactive nuclei in a given sample; it is expressed mathematically as,

  ${\text{Rate = kN}}_{\text{t}}$

Half-life period:

Half-life is defined as the time taken for amount of the sample to reduce to half of its starting value.  The symbol is ${\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}$.

$t_{\frac{1}{2}}=\frac{\ln \left(2\right)}{k}$

Half-life for a first order reaction is, $t_{\frac{1}{2}}=\frac{0.693}{k}$

(b)

Interpretation Introduction

Interpretation:

How much ${}^{90}Sr$ will remain after the half-life of 75 a if none is lost metabolically has to be found.

Concept introduction:

Half-life: The time taken for one-half of the nuclei in the sample to decay.  The half-life of the sample is independent of the quantity of radioactive material and depends on the decay constant of the nuclide in the sample.

The decay constant (k) is independent of the quantity of radioactive material however depends only on the character of the nuclide.  Various nuclides have various decay constants.  The degree of radioactive decay depends on the decay constant and number of radioactive nuclei at specific time (${\text{N}}_{\text{t}}$).  The rate of decay is directly proportional to the number of radioactive nuclei in a given sample; it is expressed mathematically as,

  ${\text{Rate = kN}}_{\text{t}}$

Half-life period:

Half-life is defined as the time taken for amount of the sample to reduce to half of its starting value.  The symbol is ${\text{t}}_{\raisebox{1ex}{$\text{1}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.}$.

$t_{\frac{1}{2}}=\frac{\ln \left(2\right)}{k}$

Half-life for a first order reaction is, $t_{\frac{1}{2}}=\frac{0.693}{k}$