Chapter 24, Problem 24.110P

Interpretation Introduction

Interpretation:

Volume of $Rn$ formed in $1\text{ h}$ at STP conditions from $1.00{\text{ g }}^{226}Ra$ has to be determined using the given information.

Concept Introduction:

• Radioactive decay is a first order reaction.
• The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\ln \text{ 2}}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$

• Decay rate can be calculated using the given equation as follows,

  $\text{A= kN}\boxed{\begin{array}{c}\text{A = Deacy rate}\\ \text{k = Deacy constant}\\ \text{N = No}\text{. of radioactive nuclei}\end{array}}$

• According to Ideal gas equation,

  $\text{Pressure}\left(P\right)\times \text{Volume}\left(V\right)\text{=}\text{Number}\text{of}\text{moles}\left(n\right)\times \text{R}\text{×}\text{Temperature}\left(T\right)$