Answer: Given information:
The half-life of a certain radioactive isotope is 50 years.
1. What is the half-life of this isotope?
The answer is straightforward: the half-life is 50 years.
2. What is the mass of the radioactive isotope at 2.0 half-lives?
After 1 half-life, the mass of the isotope will be half of the initial mass. After 2 half-lives, the mass will be half of the remaining mass, which is one-quarter of the initial mass.
Let's assume the initial mass is 100 units (it can be any value, but 100 makes the calculation easy). After 1 half-life, the mass will be 50 units. After 2 half-lives, the mass will be 25 units.
So, the mass of the radioactive isotope at 2.0 half-lives is 25 units.
3. How many half-lives occurred during the first 100 years?
Since the half-life is 50 years, we can divide 100 years by 50 years to find the number of half-lives:
100 years ÷ 50 years/half-life = 2 half-lives
Therefore, 2 half-lives occurred during the first 100 years.
Explanation:
