All natural and artificial radioactive decay of unstable nuclei follows which order kinetics?

First order

The correct answer is option 2. First order.

First-order kinetics describes a type of chemical or physical process where the rate of the reaction or decay is directly proportional to the concentration of one of the reactants or components involved. In the context of radioactive decay, it specifically refers to the rate at which unstable nuclei undergo decay to form stable nuclei.

Here is a detailed explanation:

Rate of Decay: In first-order kinetics, the rate of decay of a radioactive substance is proportional to the amount of the substance present. This means that as time progresses, the rate of decay decreases because there are fewer radioactive nuclei available to decay. Mathematically, the rate of decay (\( \frac{d[N]}{dt} \)) is proportional to the concentration of the radioactive substance (\([N]\)):

\(\frac{d[N]}{dt} = -k[N] \)

where \( k \) is the rate constant specific to the radioactive decay process.

Exponential Decay:

The solution to the differential equation for first-order kinetics results in an exponential decay function. The concentration of the radioactive substance decreases exponentially over time according to the equation:

\([N] = [N]_0 \times e^{-kt} \)

where:

\( [N] \) is the concentration of the radioactive substance at time \( t \).

\( [N]_0 \) is the initial concentration of the radioactive substance at \( t = 0 \).

\( k \) is the rate constant.

\( e \) is the base of the natural logarithm.

This equation describes how the concentration of the radioactive substance decreases with time, with a characteristic exponential decay curve.

Half-Life:

In first-order kinetics, the concept of half-life is particularly significant. The half-life (\( t_{1/2} \)) is the time required for the concentration of the radioactive substance to decrease to half of its initial value (\( [N]_0 / 2 \)). For first-order reactions, the half-life is constant and independent of the initial concentration of the substance.

Applications:

First-order kinetics is observed in various natural and artificial radioactive decay processes, including the decay of isotopes such as uranium, thorium, carbon-14, and others. It's also applicable in fields such as nuclear physics, radiology, carbon dating, and environmental science.

Overall, first-order kinetics provides a fundamental understanding of how unstable nuclei decay over time, and it's a crucial concept in the study of radioactive decay and its applications.