Sodium- 24 is a diagnostic radioisotope used to measure...

Sodium- 24 is a diagnostic radioisotope used to measure blood circulation time. Calculate the mass (mg) of a $20-\mathrm{mg}$ sample of sodium- 24 that remains after 1 day and 6 hours if sodium- 24 has $t_{1 / 2}=15$ hours.

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which the nuclei of unstable atoms lose energy by emitting radiation. This process is random for individual atoms but follows a predictable pattern for a large number of atoms, typically characterized by an exponential decay function.

Half-Life

The half-life of a radioactive isotope is the time required for half of the original quantity of the substance to decay. It is a constant for every radioactive material and is used to determine how quickly a radioactive substance diminishes over time.

Exponential Decay Equation

The exponential decay equation, usually written as M = M?(1/2)^(t/T?/?), relates the remaining mass of a radioactive substance (M) after time (t) to the initial mass (M?) by the half-life (T?/?). This equation is fundamental in calculating how much of a radioactive substance remains after a certain period of decay.

Unit Conversion

Unit conversion involves changing measurements from one unit to another to ensure consistency, particularly when the decay time is provided in different time units than the half-life. This step is important for accurate application of the exponential decay equation.

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