Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits 8 * 10^-13 J of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Verified step by step guidance

1. Step 1: Convert the radioactivity from picocuries (pCi) to disintegrations per second (dps). Use the conversion factor: 1 Curie (Ci) = 3.7 x 10^10 disintegrations per second. Since 1 pCi = 10^-12 Ci, calculate the disintegrations per second for 2 pCi.
2. Step 2: Calculate the total energy deposited in 1 year. First, find the number of disintegrations in 1 year by multiplying the disintegrations per second by the number of seconds in a year (365 days x 24 hours/day x 3600 seconds/hour). Then, multiply the total number of disintegrations by the energy deposited per alpha particle (8 x 10^-13 J).
3. Step 3: Calculate the absorbed dose in rads. The absorbed dose in rads is the energy deposited per unit mass of tissue. Use the formula: absorbed dose (rads) = (total energy deposited in joules) / (mass in kg x 0.01 J/kg).
4. Step 4: Convert the absorbed dose from rads to rems. Since the radiation weighting factor for alpha particles is 20, use the formula: dose in rems = dose in rads x radiation weighting factor.
5. Step 5: Summarize the calculations to find the number of disintegrations per second, the total energy deposited in 1 year, the absorbed dose in rads, and the dose in rems.

Key Concepts

Radioactivity and Disintegrations

Radioactivity refers to the process by which unstable atomic nuclei lose energy by emitting radiation. The activity of a radioactive substance is measured in curies (Ci) or picocuries (pCi), where 1 Ci equals 3.7 x 10^10 disintegrations per second. To find the number of disintegrations per second from a given activity level, one can convert pCi to disintegrations per second using this conversion factor.

Energy Deposition and Radiation Units

When radioactive decay occurs, energy is released in the form of radiation, which can be quantified in joules. The energy deposited by radiation in biological tissues is measured in rads, where 1 rad equals the absorption of 0.01 joules of energy per kilogram of tissue. The rem is a unit that accounts for the biological effect of radiation, factoring in the type of radiation and its impact on human health.

Calculating Radiation Exposure Over Time

To calculate the total radiation exposure over a period, such as one year, one must consider the continuous activity of the radioactive source and the energy deposited per disintegration. By determining the total number of disintegrations in a year and converting that to energy absorbed by the body, one can then express the result in rads and rems, providing a comprehensive understanding of the potential health risks associated with the exposure.