Chapter 19, Problem 19.53SP

Interpretation Introduction

Interpretation:

“The percentage of the ${}^{\text{239}}\text{Pu}$ sample that remains after the years as givenshould be found out”.

Concept introduction:

• We know that for a radioactive isotope, the amount of ${}^{\text{239}}\text{Pu}$ sample that remains after time, $\text{t}$ is: $\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{0}}}{\text{ = e}}^{\text{-λt}}$------(1)
Where, $\text{λ}$ is the decay constant and $\text{t}$ is the time of decay.

  $\begin{array}{l}{\text{N}}_{\text{t}}\text{ = sample left after time, t}\\ {\text{N}}_{\text{0}}\text{= sample present initially at t = 0}\end{array}$

  $\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{0}}}\text{ = Amount of sample left after time 't', with respect to the initial amount}$

By multiplying $100$ we will get the percentage of the sample left after given time.

Given:

The decay constant of ${}^{\text{239}}\text{Pu}$ , $\text{λ = 2}{\text{.88×10}}^{\text{-5}}{\text{ year}}^{\text{-1}}$.