Chapter 18, Problem 24AE

Interpretation Introduction

Interpretation:

Time taken for one-half of a $25\text{ g}$ sample to disappear has to be calculated.

Concept Introduction:

The term half-life is defined as the time required for a given amount of substance to be reduced half of its initial concentration. It is the characteristic property of unstable nuclide.

The formula to calculate half life of an element is as follows:

  ${\text{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{\ln 2}{\text{λ}}$        (1)

Here,

${\text{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ is radioactive half-life.

$\text{λ}$ is radioactive decay constant.

The formula to calculate time taken of decay is as follows:

    $\text{t}=\frac{\text{ln}\left(\frac{{\text{N}}_0}{\text{N}}\right)}{\text{λ}}$        (2)

Here,

${\text{N}}_0$ is initial quantity of sample.

$\text{N}$ is final quantity of sample.

$\text{λ}$ is radioactive decay constant.

$\text{t}$ is time taken for decay.