Chapter 16.5, Problem 39PP

(a)

Interpretation Introduction

Interpretation: The equation for the positron emission of $\text{Ga-68}$ needs to be determined.

Concept Introduction: When an atom on undergoing radioactive decay emits a positron particle, ${}_{+1}^0\text{β}$ from the nucleus of an atom then such type of radioactive decays is said to be positron emission.

(b)

Interpretation Introduction

Interpretation: The amount of $\text{64-mcg}$ sample that is active after $\text{136 min}$ should be calculated, if the half-life is $\text{68 min}$ .

Concept Introduction: Half-life is defined as the time taken for a radioactive substance to reach to the value which is half of its original value. The formula used is:

  ${\text{N}}_{\text{t}}{\text{ = N}}_{\text{o}}{\left(\frac{\text{1}}{\text{2}}\right)}^{\frac{\text{t}}{{\text{t}}_{\frac{\text{1}}{\text{2}}}}}$

Where ${\text{N}}_{\text{t}}$ is the quantity of the substance remaining at time $\text{t}$ , ${\text{N}}_{\text{o}}$ is the initial quantity of the substance, and ${\text{t}}_{\frac{1}{2}}$ is the half-life of the substance.