Chapter 4.1, Problem 9E

Reminder Round all answers to two decimal places unless otherwise indicated.

Half-Life of Tritium This is a continuation of Example 4.1. We stated in Example 4.1 that the half-life of a radioactive substance does not depend on the initial amount. Using the information from Example 4.1, show that it takes the same amount of time for $100\text{ grams}$ of tritium to decay to $50\text{ grams}$ as for $50\text{ grams}$ to decay to $25\text{ grams}$. How long will it take for $100\text{ grams}$ of tritium to decay to $6.25\text{ grams}$?

(Note: You can do this without your calculatorǃ)

EXAMPLE 4.1 RADIOACTIVE DECAY

Radioactive substances decay over time, and the rate of decay depends on the element. If, for example, there are $G\text{grams}$ of tritium (a radioactive form of hydrogen) in a container, then, as a result of radioactive decay, $1\text{year}$ later there will be $0.945G\text{grams}$ of tritium left.