Explain what is meant by half life. Describe the radioactivity decay law.

Half-life is a fundamental concept in nuclear physics and radiobiology that describes the time it takes for the activity or quantity of a radioactive substance to decrease by half. It is a characteristic property of each radioactive isotope and is denoted by the symbol "t₁/₂." The half-life of a radioactive substance remains constant regardless of the initial quantity present.

The radioactivity decay law describes the exponential decay of a radioactive substance over time. Mathematically, it is expressed as:

[N(t) = N0 \times \left(\frac{1}{2}\right)^{\frac{t}{t{1/2}}}]

Where:

• (N(t)) is the quantity of the radioactive substance at time (t).
• (N_0) is the initial quantity of the radioactive substance.
• (t) is the elapsed time.
• (t_{1/2}) is the half-life of the radioactive substance.

According to the decay law, the quantity of a radioactive substance decreases exponentially over time, with the rate of decay proportional to the remaining quantity of the substance. Specifically, each half-life interval results in a halving of the remaining quantity of the radioactive substance. This exponential decay process continues indefinitely, with the quantity of the substance decreasing to infinitesimally small values over successive half-life intervals.

The decay law applies to various radioactive decay processes, including alpha decay, beta decay, and gamma decay. It governs the behavior of radioactive isotopes in a wide range of applications, including radiometric dating, nuclear medicine, environmental monitoring, and nuclear power generation.

Understanding the concept of half-life and the radioactivity decay law is essential for accurately predicting the behavior of radioactive substances, assessing radiation hazards, and interpreting data from radiological measurements and experiments.