Someone is exposed to a source of \(\alpha\) radiation that results in a dose rate of \(2.0 \mathrm{mrad} \cdot \mathrm{d}^{-1}\). If nausea begins after a dose equivalent of about 100 rem, after what period will nausea become apparent?

Understanding the radiation absorbed dose, commonly referred to as 'rad', is crucial for any discussion about radiation exposure and its potential effects on the body. The rad measures the amount of energy from radiation that is deposited in a given mass of tissue. Specifically, 1 rad signifies that 0.01 joules of radiation energy has been absorbed per kilogram of tissue.

In the context of our problem, the dose rate is given in millirad (mrad), which is a thousandth of a rad. It's imperative to grasp that when working with rads, one is discussing the physical amount of energy absorbed, not the biological effects that this energy might have, which can vary depending on the type of radiation involved.

The next key concept is the 'rem', or radiation equivalent in man, which is used to account for the biological effects of different types of radiation. While the rad tells us about the pure energy absorption, the rem takes it a step further by considering the biological impact of that absorbed energy, which can vary greatly between radiation types.

For instance, one rem of alpha radiation is far more biologically damaging than one rem of gamma radiation. That's why understanding the rem is so vital—it helps us assess the potential for biological damage from a given dose of radiation. Our exercise focuses on the rem to determine the potential onset of nausea, a biological response to radiation exposure.

Alpha radiation is a type of ionizing radiation composed of helium nuclei (two protons and two neutrons). It has high energy but, due to its mass, is the least penetrating type of radiation; it can be stopped by a sheet of paper or even the outer layer of human skin.

However, once inside the body, alpha radiation can be particularly harmful due to its high ionization power—meaning it has the ability to damage biological tissues significantly. The problem with alpha radiation becomes apparent when we are discussing internal exposure, such as inhalation or ingestion of radioactive materials, where alpha emitters can cause serious harm to living cells.

Quality Factor, often denoted as 'QF', is a dimensionless multiplier used to equate the biological damage caused by different types of radiation. Since not all radiation has the same biological effect per unit absorbed dose, the QF helps us adjust the raw energy measurement (rad) into something that reflects biological impact (rem).

Alpha particles, with a typical QF of 20, are considered particularly damaging, hence their higher factor. To determine the biological equivalent dose (rem) for alpha radiation, you multiply the absorbed energy dose (rad) by the QF. In our exercise, applying this factor is essential to convert from the physical dose rate measured in mrad to a dose rate in rem that considers the biological effects of alpha radiation.