What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?

Verified step by step guidance

1. Understand the concept of half-life: The half-life of a radioactive isotope is the time it takes for half of the radioactive nuclei in a sample to decay into a more stable form.
2. Relate the half-life to strontium-90: When we say that strontium-90 has a half-life of 28.8 years, it means that after 28.8 years, half of the original amount of strontium-90 will have decayed into its daughter isotopes.
3. Express this mathematically: The decay of a radioactive isotope can be modeled using the equation \( N_t = N_0 \cdot e^{-kt} \), where \( N_t \) is the amount remaining at time \( t \), \( N_0 \) is the initial amount, \( k \) is the decay constant, and \( t \) is time.
4. Relate the decay constant to the half-life: The decay constant \( k \) is related to the half-life \( t_{1/2} \) by the formula \( k = \frac{\ln(2)}{t_{1/2}} \). For strontium-90, \( t_{1/2} = 28.8 \) years.
5. Interpret the significance: This means that if you start with a certain amount of strontium-90, after 28.8 years, only half of it will remain. After another 28.8 years (a total of 57.6 years), only one-quarter of the original amount will remain, and so on.

Key Concepts

Half-Life

Half-life is the time required for half of the radioactive atoms in a sample to decay. For strontium-90, a half-life of 28.8 years means that after this period, only half of the original amount of strontium-90 will remain, while the other half has transformed into a different element or isotope through radioactive decay.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha, beta, or gamma decay. Strontium-90 undergoes beta decay, where it transforms into a more stable isotope, releasing beta particles in the process.

Nuclear Waste Management

Nuclear waste management involves the processes of handling, storing, and disposing of radioactive waste produced by nuclear power plants. Understanding the half-life of isotopes like strontium-90 is crucial for determining safe storage durations and methods, as the waste remains hazardous for many years due to its long half-life.