Chapter 20, Problem 75AP

Interpretation Introduction

Interpretation:

The energy released during the decay of ${}^{238}\text{U}$ is to be calculated and a comparison of the velocities of ${}^{234}\text{Th}$ and $\alpha \text{-particle}$ after recoiling is to be done.

Concept introduction:

In a balanced radioactive decay

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

And,

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

The energy during the decay of a radioactive substance is given as:

$\Delta \text{E = (}\Delta {\text{m)c}}^{\text{2}}$

Here, $\Delta \text{E}$ is the amount of energy released, $\Delta \text{m}$ is the mass defect that occurs during the course of decay, and c is the speed of the light.

The mass defect ($\Delta \text{m}$) is given as the difference of total atomic mass of the product and the reactant in the balanced radioactive reaction.

Kinetic energy is defined as the energy of an object or particle that is in motion.

The kinetic energy is given as:

$\text{Kinetic energy = }\frac{1}{2}m{v}^2$

Here, $v$ is the velocity of the particle and $m$ is the mass of the particle.