Chapter 19, Problem 19.52SP

Interpretation Introduction

Interpretation:

The percentage of ${}^{\text{35}}\text{S}$ sample remains after $\text{185 days}$ should be found out.

Concept introduction:

• We know that for a radioactive isotope, the amount of ${}^{\text{35}}\text{S}$ 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 ${}^{\text{35}}\text{S}$ , $\text{λ = 7}{\text{.95×10}}^{\text{-3}}{\text{ day}}^{\text{-1}}$ and time, tis $\text{185 days}$.