Chapter 10, Problem 10.43P

Interpretation Introduction

Interpretation:

The number of half-lives elapsed in the diagram A needs to be determined.

Concept Introduction:

• Half-life − It is the time required by original radioactive element to reduce to the half of its initial concentration. Thus, at half-life ( $t_{1/2}$ )

  $\text{Concentration of reactant}=\frac{\text{ Initial concentration}}{\text{2}}$

• The decay of the radioactive element can be described by the following formula-

  $N(t)=N_0{(\frac{1}{2})}^{\frac{t}{t_{1/2}}}$

Where

N(t) − amount of reactant at time t

N₀− Initial concentration of the reactant

t_1/2 − Half-life of the decaying reactant

• The number of half-lives, $\text{n=}\frac{\text{Total time }}{\text{Half-life}}$