32.2 Biological effects of ionizing radiation  (Page 7/20)

Strategy

Dose in rem is defined by $\text{1 rad}=0\text{.}\text{01 J/kg}$ and $\text{rem}=\text{rad}\times \text{RBE}$ . The energy deposited is divided by the mass of tissue affected and then multiplied by the RBE. The latter two quantities are given, and so the main task in this example will be to find the energy deposited in one year. Since the activity of the source is given, we can calculate the number of decays, multiply by the energy per decay, and convert MeV to joules to get the total energy.

Solution

The activity $R=1\text{.}\text{00}\text{μCi}=\text{3}\text{.}\text{70}\times {\text{10}}^4\text{Bq}=3\text{.}\text{70}\times {\text{10}}^4$ decays/s. So, the number of decays per year is obtained by multiplying by the number of seconds in a year:

Thus, the ionizing energy deposited per year is

Dividing by the mass of the affected tissue gives

One Gray is 1.00 J/kg, and so the dose in Gy is

Now, the dose in Sv is

Discussion

First note that the dose is given to two digits, because the RBE is (at best) known only to two digits. By any standard, this yearly radiation dose is high and will have a devastating effect on the health of the worker. Worse yet, plutonium has a long radioactive half-life and is not readily eliminated by the body, and so it will remain in the lungs. Being an $\alpha$ emitter makes the effects 10 to 20 times worse than the same ionization produced by $\beta$ s, $\gamma$ rays, or x-rays. An activity of $1.00\mu \mathrm{Ci}$ is created by only $16\mu \mathrm{g}$ of ${}^{\text{239}}\text{Pu}$ (left as an end-of-chapter problem to verify), partly justifying claims that plutonium is the most toxic substance known. Its actual hazard depends on how likely it is to be spread out among a large population and then ingested. The Chernobyl disaster's deadly legacy, for example, has nothing to do with the plutonium it put into the environment.

Risk versus benefit

Medical doses of radiation are also limited. Diagnostic doses are generally low and have further lowered with improved techniques and faster films. With the possible exception of routine dental x-rays, radiation is used diagnostically only when needed so that the low risk is justified by the benefit of the diagnosis. Chest x-rays give the lowest doses—about 0.1 mSv to the tissue affected, with less than 5 percent scattering into tissues that are not directly imaged. Other x-ray procedures range upward to about 10 mSv in a CT scan, and about 5 mSv (0.5 rem) per dental x-ray, again both only affecting the tissue imaged. Medical images with radiopharmaceuticals give doses ranging from 1 to 5 mSv, usually localized. One exception is the thyroid scan using ${}^{\text{131}}\text{I}$ . Because of its relatively long half-life, it exposes the thyroid to about 0.75 Sv. The isotope ${}^{\text{123}}\text{I}$ is more difficult to produce, but its short half-life limits thyroid exposure to about 15 mSv.

Phet explorations: alpha decay

Watch alpha particles escape from a polonium nucleus, causing radioactive alpha decay. See how random decay times relate to the half life.