Chapter 17, Problem 74E

Interpretation Introduction

Interpretation:

The amount of time required for the decay of theU-235 (uranium isotope) to one eighth of its initial amount with a half-life of $703\text{ million years }$ is to be determined.

Concept introduction:

The half-life of a substance is the numerical value in which the given radioactive substance is assumed to be reduced to half of its initial amount. The half-life for a given substance is represented by t_1/2.

In case, the decay of a radioactive substance is exponential, it will remain constant for the life time of the substance.

After each half-life period, the amount of the substance is reduced to half of the initial number.

The time required for the decay of the substance to a given amount of substance can be calculated using the formula mentioned below:

${\text{N}}_{\text{t}}={\text{N}}_{\text{0}}\times {\text{e}}^{\left(\frac{-\text{0}\text{.693}\times \text{t}}{\text{k}}\right)}$

In the above equation, ‘N_t’ represents the mass of the radioactive substance after a certain time interval t, ‘N₀’ indicates the initial mass of the radioactive material, ‘k’ represents the decay constant and ‘t’ represents the time required to reach the value of N_t.