The maximum radon level in drinking water is 4.0 pCi per milliliter, which corresponds to 0.148 disintegrations per second. The number of 222Rn atoms in 1.00 mL of water cannot be determined without the initial number of atoms (N₀).
To determine the number of disintegrations per second and the number of 222Rn atoms in 1.00 mL of water, we can use the given information.
1. Number of disintegrations per second:
The maximum radon level in drinking water is 4.0 pCi (picocuries) per milliliter. A picocurie is a unit of radioactivity. To calculate the number of disintegrations per second, we need to convert picocuries to becquerels (Bq), which is the SI unit of radioactivity.
1 Ci (curie) = 3.7 x 10^10 Bq
1 pCi = 0.037 Bq
Therefore, 4.0 pCi = 0.037 x 4.0 Bq = 0.148 Bq
So, there would be 0.148 disintegrations per second in a milliliter of water for this level of radon radioactivity.
2. Number of 222Rn atoms in 1.00 mL of water:
To calculate the number of 222Rn atoms, we need to consider the half-life of 222Rn, which is given as 3.8 days.
The number of radioactive atoms can be calculated using the equation:
N = N₀ * (1/2)^(t/t₁/₂)
Where:
N₀ is the initial number of atoms
N is the final number of atoms
t is the time elapsed
t₁/₂ is the half-life
In this case, the final number of atoms (N) would be the number of 222Rn atoms in 1.00 mL of water.
Using the given half-life (3.8 days), we can calculate the number of 222Rn atoms.
N = N₀ * (1/2)^(t/t₁/₂)
N = N₀ * (1/2)^(1/1.9)
Since the initial number of atoms (N₀) is not given, we cannot calculate the exact number of 222Rn atoms in 1.00 mL of water without that information.