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Radon is a colorless, odorless radioactive gas that originates from the decay of uranium, which is found in different amounts in soil and rock throughout the world. Radon in drinking water primarily comes from groundwater sources, such as wells that tap into aquifers containing natural uranium deposits. When water containing radon is used in households for showers, cooking, and laundry, the radon can be released into the indoor air, posing a risk of inhalation.

In 1999, concerned about the health risks associated with radon exposure, the U.S. Environmental Protection Agency (EPA) set a maximum contaminant level for radon in drinking water at 4.0 pCi per milliliter. The pCi (picocurie) is a measure of radioactivity representing the decay of a certain number of atoms per second. Therefore, when considering the safety of drinking water, it's crucial to understand not just the presence of radon, but the level at which it occurs and the potential for decay events that can lead to radiation exposure.

When discussing radioactivity, one of the fundamental measurements is the number of decay events per second. A decay event occurs when an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This process is random for each atom, but the rate at which decay events occur can be estimated for a group of radioactive atoms.

The unit Bequerel (Bq) defines one decay event per second. To relate this to practical situations, such as the safety limits for radon in drinking water, the conversion factor between pCi and Bq is used. In our case, 1 pCi equals 3.7×10^−2 Bq (the international standard), allowing us to express the EPA's limit in terms of the number of decay events that are happening every second. For an acceptable radon level of 4.0 pCi/mL, we would calculate the decay events per second to ensure the water meets safety standards.

To calculate the specific quantity of radioactive atoms present in a sample of material, such as a milliliter of water, we can use the radioactive decay formula. The core of this formula involves the decay constant (λ), which is unique to each radioactive isotope and represents the probability of decay occurring for an atom at any given instant.

Finding the Decay Constant

The formula for the decay constant is \(\lambda = \frac{\ln(2)}{t_{1/2}}\), where \(t_{1/2}\) is the half-life of the isotope, or the time it takes for half the atoms in a sample to undergo decay. Knowing the half-life allows us to calculate the decay constant, which then helps us work out the number of radioactive atoms present by rearranging the decay formula: \(\text{Activity} = \lambda \times N\). Activity is the number of decay events occurring per second, measured in Bq, and N is the number of atoms. Solving for N gives us the number of radon atoms in our water sample, showing the direct relationship between the decay constant, the radioactive decay formula, and the assessment of radon levels in water.