If a gallon container has an air concentration of 4 pCi/L, approximately how many disintegrations per minute of radon atoms are present?

To determine the number of disintegrations per minute (DPM) of radon atoms present in a gallon container with an air concentration of 4 pCi/L, it is important to understand the relationship between picocuries and disintegrations.

1. The unit of picocurie (pCi) reflects the radioactivity of a substance, specifically defined as 1 picocurie being equal to 2.22 disintegrations per minute. Therefore, to convert a concentration measured in pCi/L to DPM, you can multiply the concentration by the conversion factor.

2. In this scenario, with a concentration of 4 pCi/L, the conversion calculation would be:

[ 4 \text{ pCi/L} \times 2.22 \text{ DPM/pCi} = 8.88 \text{ DPM} ]

3. However, since this is based on air concentration in a liter and the question specifies a gallon container, it's essential to convert gallons to liters because the pCi concentration given pertains to a volume of 1 liter.

4. There are roughly 3.78541 liters in a gallon. Therefore, to find the total DPM for one gallon containing