To determine the activity of a radioactive substance, we utilize the equation:

$A = \lambda N$

In this equation, $A$ represents the activity, $\lambda$ denotes the decay constant, and $N$ signifies the number of radioactive atoms present in the sample.

Radioactivity is a phenomenon in which unstable atomic nuclei emit particles or electromagnetic radiation. The activity of a radioactive substance quantifies the rate at which it emits radiation, and it is measured in becquerels (Bq). Specifically, one becquerel corresponds to one decay event occurring per second.

The decay constant, $\lambda$, serves as an indicator of how rapidly a radioactive substance undergoes decay. It is defined as the probability of decay per unit time and is expressed in reciprocal seconds ($\text{s}^{-1}$). The value of $\lambda$ is unique to each radioactive isotope and varies accordingly.

The term $N$ refers to the count of radioactive atoms in the sample that are capable of undergoing radioactive decay. This can be expressed in terms of moles or as an absolute number of atoms.

To calculate the activity of a radioactive substance, we simply multiply the decay constant $\lambda$ by the number of radioactive atoms $N$ in the sample. This calculation yields the rate at which the substance is emitting radiation, which is its activity.

It is crucial to recognize that the activity of a radioactive substance diminishes over time as the number of radioactive atoms decreases due to decay. This decrease is described by the exponential decay equation:

$N(t) = N_0 e^{-\lambda t}$

In this formula, $N_0$ represents the initial quantity of radioactive atoms, and $t$ is the time elapsed. By applying this equation, we can determine the activity of a radioactive substance at any specific moment in time.