Chapter 20, Problem 66AP

Interpretation Introduction

Interpretation:

The activity of $0.500\text{ g}$ ${{}^{\text{237}}}_{\text{93}}\text{Np}$ is to be determined and the balanced nuclear decay reaction for ${{}^{\text{237}}}_{\text{93}}\text{Np}$ is to be represented.

Concept introduction:

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

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

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

All radioactive decay is of the first order and its rate constant is given as follows:

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

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

In a balanced radioactive decay,

${\displaystyle \sum \text{Reactant mass number = }{\displaystyle \sum \text{Product mass number}}}$

${\displaystyle \sum \text{Reactant atomic number = }{\displaystyle \sum \text{Product atomic number}}}$

In a balanced radioactive decay equation, the subscript present on the individual particles represents the atomic number, while the superscript represents the atomic mass.