Question

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 \(8 \times 10^{-13} \mathrm{J}\) 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.

Short answer

The number of disintegrations per second due to 2 pCi of plutonium radioactivity is \(2 \times 3.7 \times 10^{-2}\) dps. The total energy deposited per second is this value multiplied by \(8 \times 10^{-13}\) J, and the energy deposited per year can be found by multiplying it by the number of seconds in a year. To calculate the dose of radiation in rads, divide the energy per year by (75 kg × 0.01 J/kg). To find the dose in rems, multiply the dose in rads by the quality factor for alpha particles (20).

Step-by-step solution

Calculate disintegrations per second

To find the disintegrations per second, we need to understand that the unit pCi stands for picocuries which are a measure of radioactivity. We are given that the average person contains 2 pCi of plutonium radioactivity. 1 pCi is equivalent to \(3.7 \times 10^{-2}\) disintegrations per second (dps). To find the disintegrations per second of the 2 pCi of plutonium, we can multiply the given plutonium radioactivity by the conversion factor: - Disintegrations per second = (2 pCi) × \(3.7 \times 10^{-2}\) dps/pCi

Calculate energy deposited per second

We are told that each alpha particle deposits \(8 \times 10^{-13}\) J of energy. To find the total energy deposited per second, multiply the number of disintegrations per second found in step 1 by the energy deposited per alpha particle: - Energy per second = (Disintegrations per second) × \(8 \times 10^{-13}\) J

Calculate energy deposited per year

Next, we want to find the total energy deposited in 1 year. To do this, we need to multiply the energy per second by the number of seconds in a year: - Energy per year = (Energy per second) × (Number of seconds in a year) - Number of seconds in a year = 365 days × 24 hours/day × 3600 seconds/hour

Calculate dose in rads and rems

Now that we have the energy deposited per year, we can use this information to calculate the dose of radiation in rads and rems. 1 rad = 0.01 J/kg 1 rem = 1 rad × (Quality factor for alpha particles) The quality factor for alpha particles is 20. - Dose in rads = (Energy per year) / (75 kg × 0.01 J/kg) - Dose in rems = (Dose in rads) × (Quality factor for alpha particles) Finally, we will be able to find the number of rads and rems of radiation in 1 year from the given level of plutonium.

Key concepts

Picocuries

Picocuries (pCi) are a unit used to measure radioactivity, named in honor of Marie and Pierre Curie who were pioneers in the research of radioactive elements. One picocurie represents the radioactivity caused by one trillionth of a curie, which is itself defined as the amount of a radioactive isotope that decays at a rate of 37 billion disintegrations per second (dps). The term 'picocurie' is essential in monitoring environmental radioactivity as well as in medical diagnostics and treatments involving radioactive substances.

To illustrate: if a substance has an activity of 2 pCi, this means that in one second, there are approximately 74 (i.e., 2 x 37) radioactive disintegrations occurring. Thus, it is a very sensitive unit, capable of detecting minute levels of radioactivity, which is critical when measuring radiation levels in biological and environmental contexts for the protection of human health.

Disintegrations Per Second

Disintegrations per second is a direct measure of radioactivity. This unit quantifies the number of atoms in a radioactive substance that decay within one second and is crucial in identifying the intensity of the radioactivity of a sample. Radioactivity is a natural process by which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves.

In a practical sense, understanding and calculating disintegrations per second allows us to quantify the level of radioactive exposure. For instance, from the textbook example, the disintegration from plutonium radioactivity in the human body is calculated using the picocurie measurement. Simply put, if a sample is said to have 2 picocuries of radioactivity, this translates to a calculated number of disintegrations (radioactive events) each second, which can then be used to determine the radiation dose absorbed by that body.

Rads and Rems

When discussing radioactivity and its effects on material, 'rads' and 'rems' are units of measure for the absorbed dose and the effective biological damage, respectively. Specifically, the rad (radiation absorbed dose) quantifies the amount of energy that radioactive material deposits in a target, typically measured in joules per kilogram. A rad is defined as an absorption of 0.01 joules of energy per kilogram of target material. It describes the energy imparted but does not account for the biological effects of different types of radiation.

For considering biological impact, we use the unit 'rem' (roentgen equivalent man), which takes into account the type of radiation and its potential for biological damage. Essentially, it is a product of the dose in rads and a quality factor that's specific to the type of radiation involved. This factor represents the relative biological effectiveness (RBE) of the radiation, which varies with the type of radiation; for example, alpha particles have a high quality factor due to their high ionizing power and biological damage potential. The conversion from rads to rems involves multiplying by the quality factor, giving a more accurate representation of potential damage to human tissue.

Plutonium Radioactivity

Plutonium is a heavy, radioactive metallic element that is used in nuclear reactors and weapons. Its radioactivity comes from unstable isotopes that can emit alpha, beta, and gamma radiation during their decay process. The radioactivity of plutonium is a major concern due to its long half-life and the intense alpha radiation it emits, which, although not penetrating, can cause significant damage to living tissue if ingested or inhaled.

Understanding the radioactivity of plutonium is key for both radiation protection and environmental safety. The calculations provided in the original exercise help determine the biological impact of plutonium exposure on the human body, measured in terms of rads and rems. These calculations are crucial for enforcing safety regulations, assessing contamination levels, and devising medical treatment for exposed individuals. With advancements in detection and measurement, it's possible to estimate the radioactivity levels within biological specimens, even at the tiny levels represented by picocuries of plutonium.