Chapter 39, Problem 60A

If a sample of radioactive material has a half-life of one week, how much of the original sample will be left at the end of the second week? The third week? The fourth week?

To determine

The amount of the radioactive material at the end of second week, third week and fourth week.

Explanation of Solution

Introduction:

The duration in which the amount of radioactive material reduces to half of initial amount is called the half-life of radioactive material.

The amount becomes half of initial amount in duration of half-life of radioactive material. The half-life of the radioactive material is one week. The amount of radioactive material become half in one week.

The half amount of material becomes initial amount for the second week. This half amount of radioactive material from first week again becomes half. So, the amount of the radioactive material at the end of second week becomes one-fourth of initial amount of radioactive material.

The amount of the radioactive material at the end of third week becomes half of the amount of radioactive material of second week. The amount of the radioactive material at the end of third week is one-eighth of initial amount at the beginning of first week.

The amount of the radioactive material at the end of fourth week is one-sixteenth of initial amount at the beginning of first week.

Conclusion:

Thus, the amount of the radioactive material at the end of second week is one-fourth, at the end of third week is one-eighth and at the fourth week is one-sixteenth of initial amount at the beginning of first week.