How is a radioactive isotope’s half-life related to its decay constant?

The decay constant ($\lambda$) and the half-life ($T_{1/2}$) of a radioactive isotope are inversely related, representing the rate at which a population of unstable nuclei decays over time.12

Mathematically, this relationship is expressed as:
$$T_{1/2}=\frac{\ln (2)}{\lambda }\approx \frac{0.693}{\lambda }$$

In this context, the decay constant $\lambda$ represents the proportionality between the size of a radioactive population and its rate of decrease, while the half-life is the specific time interval required for that population to reduce by half. Because radioactive decay is a statistical exponential process, these two values provide equivalent ways to describe the stability and transition rate of a given nuclide.123