The half-life of I- 131 is 8.0 days. A sample containing...

The half-life of I- 131 is $8.0$ days. A sample containing I-131 has an activity of $6.4 \times 10^{8}$ Bq. How many days later will the sample have an activity of $2.5 \times 10^{6} \mathrm{~Bq}$ ?

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Key Concepts

Logarithmic Functions

Logarithms are used to solve the exponential decay equation for time. When the decay equation is set up with given initial and remaining activities, taking the natural logarithm of both sides allows isolation and calculation of the time variable, completing the solution process.

Radioactive Decay

This is the process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. The decay occurs at a rate that is proportional to the amount of the substance present, meaning the quantity decreases exponentially over time.

Half-Life

The half-life of a radioactive substance is the time required for half of the atoms in a sample to undergo decay. It is a characteristic measure that helps quantify the rate at which the radioactivity decreases and is independent of the initial amount.

Exponential Decay Equation

This mathematical equation describes the decay process over time, typically expressed as N(t) = N0 * e^(-?t), where N0 is the initial quantity, N(t) is the remaining quantity at time t, and ? (lambda) is the decay constant related to the half-life. It is essential for solving problems related to the reduction of the substance over time.

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