Chapter 20, Problem 77AP

Interpretation Introduction

Interpretation:

The value of Avogadro’s number is to be determined, for the given molar mass of ${{}^{226}}_{}\text{Ra}$ and its half-life, using the definition of 1 curie.

Concept Introduction:

The rate of decay for a particular isotope is given by the rate law as:

$\text{Rate = }k\text{N}$

Here, $k$ is the rate constant for the radioactive decay and $\text{N}$ is the number of atoms in the sample.

Nearly the entirety of radioactive decay is of the first order and its rate constant is given as:

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

Here, $t_{1/2}$ is the half-life of the radioactive substance.

One curie is defined as $3.7\times {\text{ 10}}^{\text{10}}$ disintegration occurring per second, which is nearly equal to the rate of decay of 1 g radium.