Assume a liter of milk has an activity of 2400 pCi due to 40K. If a person drinks 2 glasses (0.460 l) per day, estimate the total dose (rem) received in a year. As a crude model, assume the milk stays in the stomach 13.5hr and is then released. Assume also that 15.0 percent of the 1.50 MeV released per decay is absorbed by the body. Calculate the dose in mrem. Make your calculation assuming this person is a 68.8 kg adult.

To calculate the total dose (in millirems, or mrem) received in a year, we need to consider a few factors: the activity of the milk, the amount of milk consumed per day, the time it stays in the stomach, the energy released per decay, and the absorption percentage.

Let's break down the calculation step by step.

1. Activity of the milk (A): Given that a liter of milk has an activity of 2400 pCi (picocuries) due to 40K.

2. Amount of milk consumed per day (V): Each day, the person drinks 2 glasses of milk, which is equivalent to 0.460 liters.

3. Decay time in the stomach (t): Given that the milk stays in the stomach for 13.5 hours.

4. Energy released per decay (E): We're told that 15.0 percent of the 1.50 MeV (megaelectronvolts) released per decay is absorbed by the body.

5. Weight of the person (w): Given that the person weighs 68.8 kg.

Now, let's calculate the dose in mrem using the formula:

Dose (in mrem) = (A * V * t * E * 0.15) / w

First, we need to convert the activity from picocuries (pCi) to curies (Ci):
Activity (in Ci) = Activity (in pCi) * 10^(-12)

1. Converting activity to Ci:
Activity = 2400 pCi * 10^(-12) = 2.4 * 10^(-9) Ci

2. Dose calculation:
Dose = (2.4 * 10^(-9) Ci * 0.460 l * (13.5 hours / 24 hours) * 1.50 MeV * 0.15) / 68.8 kg

Note: We convert the decay time to a fraction of a day by dividing it by 24 hours.

Simplifying the equation:
Dose = (2.4 * 10^(-9) * 0.460 * (13.5 / 24) * 1.50 * 0.15) / 68.8

Calculating the result:
Dose ≈ 5.00 * 10^(-11) mrem

Therefore, the estimated total dose received in a year is approximately 5.00 * 10^(-11) mrem.