Strontium-90 Decay Over Time: Calculating Molecular Fractions and Decay Rates

Understanding the decay behavior of radioactive isotopes like 90Sr is crucial in fields such as nuclear physics, environmental science, and radiological medicine. This article will explore how to determine the fraction of a mole of 90Sr remaining after a specific period, using both the half-life method and the decay constant approach.

Key Concepts: Half-Life and Decay Rate

Nuclear decay is governed by the concept of half-life, which is the time required for half of a radioactive substance to decay to its daughter product. For 90Sr, the half-life is approximately 28.8 years. This information can be derived from various sources, including scientific publications and reliable online resources. The half-life is a fundamental parameter in understanding the decay process.

Decay Process: Basic Mathematical Principles

Let's consider the decay of one mole of 90Sr over a period of 112 years. The decay rate, or activity, can be described using the decay constant and the initial number of atoms. The decay constant, k, is related to the half-life (t1/2) by the equation: k ln(2) / t1/2.

Method 1: Using the Half-Life

The first method involves using the concept of half-lives. After 112 years, we need to determine how many half-lives have passed and then calculate the remaining moles of Sr-90.

Step 1: Calculate the number of half-lives:

N 112 yr / 28.8 yr 3.89 half-lives

Step 2: Determine the remaining moles of Sr-90:

Nremaining N × (1/2)^N

Nremaining 1 mol × (1/2)3.89 ≈ 0.0675 mol

Method 2: Using the Decay Constant

The second method involves using the decay constant (k) and the exponential decay formula. The decay constant is given by:

k ln(2) / t1/2 ln(2) / 28.8 yr 0.02407 yr-1

The exponential decay formula is:

Nremaining N × e-kt

Step 1: Determine the decay time (t): t 112 yr

Step 2: Calculate the remaining moles of Sr-90:

Nremaining 1 × e-0.02407 × 112 ≈ 0.0675 mol

Understanding the Concepts

It's important to clarify that atoms do not 'disinterest' themselves; rather, they decay according to their inherent properties. The term 'proof-reading' refers to verifying and correcting errors in writing, which is not directly applicable to the decay of radioactive substances.

Calculating the Fraction of Remaining Moles

Using the calculations above, we can determine that after 112 years, about 6.75% of the initial mole of 90Sr remains. This fraction can be derived by calculating 1/(23.89) or approximately 1/16th of the original mole.

Conclusion

The decay behavior of 90Sr and other radioactive isotopes can be analyzed using both half-life and decay constant methods. Understanding these concepts is essential for predicting the long-term behavior of radioactive substances and their impact on the environment and health.

Related Keywords

strontium-90 half-life decay rate

For further reading on related topics, consider exploring scientific literature, educational articles, and online resources dedicated to nuclear physics and radiological sciences.