Chapter 21.8, Problem 21.3WE

Interpretation Introduction

Interpretation: The quantity of Rn-222 after 10 half-lives should be determined. Initial concentration of the given substance and its half-life is given.

Concept Introduction:

•   Half-life ( ${\text{t}}_{\frac{\text{1}}{\text{2}}}$) is the time required for a quantity to reduce to half its initial value.
• Order of a reaction is the sum of powers of the concentration terms in the rate equation.
  • That is for general reaction $\text{aA}\text{+}\text{bB}\to \text{product}$,
•         $\text{Rate}\text{=}\text{k}{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}$             k is the rate constant.
• Order of the reaction = a + b
• Rate of a first order reaction is depending only on the concentration of one reactant.
• All radioactive decays obey first order kinetics.
• An unstable nucleus emits radiation spontaneously to become stable nuclei by losing energy. This process of emission of radiation by unstable nuclei is known as radioactive decay.
• In general the substance left after n half –lives is  ${\left(\frac{\text{1}}{\text{2}}\right)}^{\text{n}}$.

To determine: The quantity of Rn-222 left after radioactive decay.