49 After decaying for 48 hours, l/16 of the original mass of a radioisotope sample remains unchanged. What is the half-life of this radioisotope? (1) 3.0 h (3) 12 h(2) 9.6 h (4) 24 h
The correct answer and explanation is:
Correct Answer: (3) 12 h
To find the half-life of a radioisotope, we use the concept that the amount of a radioactive substance decreases by half after each half-life period. In this problem, after 48 hours, only 1/16 of the original mass remains. This fraction helps us determine how many half-lives have passed.
We start by understanding the pattern:
- After 1 half-life: 1/2 remains
- After 2 half-lives: 1/4 remains
- After 3 half-lives: 1/8 remains
- After 4 half-lives: 1/16 remains
So, we can clearly see that 4 half-lives have passed in 48 hours. To find the length of one half-life, divide the total time by the number of half-lives: Half-life=48 hours4=12 hours\text{Half-life} = \frac{48\ \text{hours}}{4} = 12\ \text{hours}
Thus, the correct half-life of this radioisotope is 12 hours.
This calculation is important in nuclear chemistry and physics. The half-life is a constant value for a given isotope and does not depend on the amount of substance or external conditions like temperature or pressure. It is a measure of how quickly a radioactive substance undergoes decay. By understanding how many half-lives have passed, scientists can estimate how much of a sample remains and how long it will take for a substance to become safe or non-radioactive.
This concept is also used in medicine (radioactive tracers), archaeology (carbon dating), and environmental science (nuclear waste management). In all these fields, calculating half-lives allows accurate tracking of how a substance behaves over time.