Calculate the dose in rem/y for the lungs of a weapons plant employee who inhales and retains an activity of \(1.00 \mu \mathrm{Ci}^{239} \mathrm{Pu}\) in an accident. The mass of affected lung tissue is \(2.00 \mathrm{kg}\) and the plutonium decays by emission of a 5.23-MeV \(\alpha\) particle. Assume a RBE value of 20.

When we refer to 'activity' in radiation physics, we are talking about how many nuclear decays occur in a material over time. This rate of decay is crucial for determining how much radiation is released by a radioactive source. To accurately calculate activity, which is measured in becquerels (Bq), one must consider the type and amount of radioactive material.

For example, in the exercise provided, the activity of plutonium-239 is converted from microcuries to becquerels using the conversion factor of 1 curie (Ci) to 3.7 x 10¹⁰ Bq. Understanding this conversion is essential, as different units are used depending on the context. Health physicists, engineers, and technicians rely on these calculations to ensure safety and compliance with regulatory limits.

Dealing with radioactive materials often requires conversions between different units of energy. Energy released in radioactive decay is typically given in megaelectronvolts (MeV), a unit common in nuclear physics. To relate this energy to other forms such as heat or work, it is often necessary to convert MeV to joules (J), the SI unit of energy and work.

In the provided example, each decay releases 5.23 MeV of energy, which is then converted to joules using the factor that 1 eV equals 1.602 x 10^-19 joules. This step is vital for further calculations, such as determining the absorbed dose, because it places the radioactive decay energy in a context understandable in terms of the effects on human tissue or other materials.

The absorbed dose is a measure of the radiation energy absorbed per unit mass of tissue and is expressed in the unit gray (Gy). It is a critical concept for understanding the potential for biological damage from exposure to radiation. One gray is equivalent to the absorption of one joule of radiation energy by one kilogram of matter.

In practical terms, as seen in our example, it's important to divide the total energy deposited in the tissue (in joules) by the mass of the tissue (in kilograms) to obtain the absorbed dose in grays. However, to fully assess the potential biological effects of the radiation, one must also consider the type of radiation involved, which is where the concept of relative biological effectiveness comes into play.

The concept of Relative Biological Effectiveness (RBE) is used to compare the biological damage caused by different types of ionizing radiation. Not all radiation has the same effect on living tissue; for instance, alpha particles are much more damaging than beta particles or gamma rays when they all deposit the same energy in a tissue.

In our scenario, the RBE for alpha particles is given as 20 times more damaging than the standard reference of 1 for x-rays. Thus, the absorbed dose in gray must be multiplied by the RBE to convert it to an equivalent dose in rems (or sieverts in SI units), which better represents the biological risk. The practice of considering RBE is essential for ensuring that safety standards and radiological protections reflect the true potential for harm from different types of radiation exposure.