Chapter 20, Problem 28QP

Interpretation Introduction

Interpretation:

The half-life of isolated sample of ${}^{90}\text{Y}$ is to be calculated.

Concept introduction:

The time required for a chemical species to reduce to half of its initial value is termed as half-life.

All radioactive decay follow first order kinetics. The decay is proportional to the amount of the radioisotope at any time.

The half-life is calculated by the expression as follows:

$t_{1/2}=\frac{0.693}{k}$

Here, $t_{1/2}$ is the half-life and $k$ is the rate constant.

The expression for the rate constant is represented as follows:

$\ln \frac{N_t}{N_o}\text{ =}-kt$

Here, $k$ is the rate constant, $t$ is the time for the reaction, $N_o$ is the initial concentration of the reactant, and $N_t$ is the concentration of the reactant after time $t$.