How to Calculate Half-life in Radioactive Decay Kinetics

Understanding how to calculate the half-life of a radioactive substance is essential in nuclear physics and related fields. The half-life indicates the time required for half of the radioactive atoms to decay. This article explains the basic method to determine the half-life using decay equations.

Basic Decay Equation

The decay of a radioactive substance follows an exponential law. The number of remaining radioactive atoms at time t can be expressed as:

N(t) = N₀ e^-λt

Where N₀ is the initial number of atoms, λ is the decay constant, and t is time.

Calculating Half-Life

The half-life (T_1/2) is the time when N(t) equals half of N₀. Setting N(t) = N₀/2 in the decay equation gives:

1/2 = e^-λT_1/2

Taking the natural logarithm of both sides results in:

ln(1/2) = -λT_1/2

Since ln(1/2) = -0.693, the formula for half-life becomes:

T_1/2 = 0.693 / λ

Determining the Decay Constant

The decay constant λ can be found if the half-life is known, or it can be calculated from experimental data. If the decay constant is unknown, it can be derived from measurements of activity or remaining atoms over time.

Once λ is known, calculating the half-life is straightforward using the formula above.