A sample of sodium-24 was administered to a patient to test...

A sample of sodium-24 was administered to a patient to test for faulty blood circulation by comparing the radioactivity reaching various parts of the body. What fraction of the sodium-24 nuclei would remain undecayed after $12.0 \mathrm{~h} ?$ The half-life is 15.0h. If a sample contains $6.0 \mu \mathrm{g}$ of ${ }^{24} \mathrm{Na}$, how many micrograms remain after $12.0 \mathrm{~h}$ ?

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Key Concepts

Radioactive Tracer Technique

Radioactive tracer techniques involve the use of radioactive substances to track or image processes within a system, such as blood circulation in the body. By monitoring the decay or distribution of the tracer, researchers and medical professionals can gain insights into the function and dynamics of biological systems. This application leverages the predictable decay behavior described by the exponential decay law and half-life.

Half-life

Half-life is the time required for half of the nuclei in a radioactive substance to decay. It is a characteristic property of each radioactive isotope and provides a measure of the rate at which a substance undergoes radioactive decay. This concept is fundamental in both nuclear physics and in applications such as medical diagnostics and treatment planning.

Exponential Decay Law

The exponential decay law describes how the number of radioactive nuclei decreases over time. It is mathematically represented as N = N?(1/2)^(t/T?/?), where N? is the initial quantity, t is the elapsed time, and T?/? is the half-life. This law is used to calculate the remaining quantity of a substance after a given period, making it essential for understanding and predicting radioactive decay processes.

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