Radioactive Decay: Calculating the Age of Uranium-235 Sample

How can we determine the age of a uranium-235 sample based on its radioactive decay?

Calculate the age of the sample when its activity decreases to 194 mCi from an initial 12,435 mCi.

Calculating the Age of Uranium-235 Sample

The age of the uranium-235 sample can be determined using the decay formula combined with the known half-life of uranium-235. This involves calculating the decay constant, inserting the given values into a simplified decay formula, and solving for time.

The subject of radioactive decay of uranium-235 involves understanding how the activity of a sample changes over time. In this case, we are provided with the initial activity of 12,435 mCi and the final activity of 194 mCi. To determine the age of the sample, we need to utilize the concept of half-life, which is a fundamental property of radioactive elements.

The half-life of uranium-235 is approximately 703.8 million years. This means that over a period of 703.8 million years, half of the initial amount of uranium-235 will decay. By understanding this principle, we can calculate the decay constant (λ) using the equation λ = ln(2) / half-life.

Subsequently, we can use the decay equation N = N0 * e^(-λt), where N is the final activity, N0 is the initial activity, λ is the decay constant, and t is the time. By rearranging the equation and substituting the given values, we can solve for the age of the uranium-235 sample when its activity drops to 194 mCi.

By applying the decay equation and the calculated decay constant, we can accurately determine the age of the uranium-235 sample based on its radioactive decay. This process provides insights into the history and decay timeline of the sample, showcasing the fascinating properties of radioactive elements like uranium-235.