# 32.2 Biological effects of ionizing radiation  (Page 7/19)

 Page 7 / 19

Strategy

Dose in rem is defined by $\text{1 rad}=0\text{.}\text{01 J/kg}$ and $\text{rem}=\text{rad}×\text{RBE}$ . 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 $R=1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μCi}=\text{3}\text{.}\text{70}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{Bq}=3\text{.}\text{70}×{\text{10}}^{4}$ decays/s. So, the number of decays per year is obtained by multiplying by the number of seconds in a year:

$\left(3\text{.}\text{70}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{decays/s}\right)\left(3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s}\right)=1\text{.}\text{17}×{\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{decays.}$

Thus, the ionizing energy deposited per year is

$E=\left(1\text{.}\text{17}×{\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{decays}\right)\left(5\text{.}\text{23}\phantom{\rule{0.25em}{0ex}}\text{MeV/decay}\right)×\left(\frac{1.60×{\text{10}}^{-\text{13}}\phantom{\rule{0.25em}{0ex}}\text{J}}{\text{MeV}}\right)=0\text{.}\text{978}\phantom{\rule{0.25em}{0ex}}\text{J.}$

Dividing by the mass of the affected tissue gives

$\frac{E}{\text{mass}}=\frac{0\text{.}\text{978}\phantom{\rule{0.25em}{0ex}}\text{J}}{2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{kg}}=0\text{.}\text{489 J/kg.}$

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

$\text{dose in Gy}=\frac{\text{0.489}\phantom{\rule{0.25em}{0ex}}\text{J/kg}}{1.00\phantom{\rule{0.25em}{0ex}}\text{(J/kg)/Gy}}=0.489 Gy.$

Now, the dose in Sv is

$=\left(0.489 Gy\right)\left(\text{20}\right)=\text{9.8 Sv.}$

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 $1.00\phantom{\rule{0.25em}{0ex}}\mu Ci$ is created by only $16\phantom{\rule{0.25em}{0ex}}\mu g$ 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.

## Section summary

• The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction, and destruction of cell function.
• A radiation dose unit called the rad is defined in terms of the ionizing energy deposited per kilogram of tissue:
$1 rad=\text{0.01 J/kg}.$
• The SI unit for radiation dose is the gray (Gy), which is defined to be $1 Gy = 1 J/kg = 100 rad.$
• To account for the effect of the type of particle creating the ionization, we use the relative biological effectiveness (RBE) or quality factor (QF) given in [link] and define a unit called the roentgen equivalent man (rem) as
$\text{rem}=\text{rad}×\text{RBE}.$
• Particles that have short ranges or create large ionization densities have RBEs greater than unity. The SI equivalent of the rem is the sievert (Sv), defined to be
• Whole-body, single-exposure doses of 0.1 Sv or less are low doses while those of 0.1 to 1 Sv are moderate, and those over 1 Sv are high doses. Some immediate radiation effects are given in [link] . Effects due to low doses are not observed, but their risk is assumed to be directly proportional to those of high doses, an assumption known as the linear hypothesis. Long-term effects are cancer deaths at the rate of $\text{10}/{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{rem·y}$ and genetic defects at roughly one-third this rate. Background radiation doses and sources are given in [link] . World-wide average radiation exposure from natural sources, including radon, is about 3 mSv, or 300 mrem. Radiation protection utilizes shielding, distance, and time to limit exposure.

## Conceptual questions

Isotopes that emit $\alpha$ radiation are relatively safe outside the body and exceptionally hazardous inside. Yet those that emit $\gamma$ radiation are hazardous outside and inside. Explain why.

Why is radon more closely associated with inducing lung cancer than other types of cancer?

The RBE for low-energy $\beta$ s is 1.7, whereas that for higher-energy $\beta$ s is only 1. Explain why, considering how the range of radiation depends on its energy.

Which methods of radiation protection were used in the device shown in the first photo in [link] ? Which were used in the situation shown in the second photo?

(a)

What radioisotope could be a problem in homes built of cinder blocks made from uranium mine tailings? (This is true of homes and schools in certain regions near uranium mines.)

Are some types of cancer more sensitive to radiation than others? If so, what makes them more sensitive?

Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?

## Problems&Exercises

What is the dose in mSv for: (a) a 0.1 Gy x-ray? (b) 2.5 mGy of neutron exposure to the eye? (c) 1.5 mGy of $\alpha$ exposure?

(a) 100 mSv

(b) 80 mSv

(c) ~30 mSv

Find the radiation dose in Gy for: (a) A 10-mSv fluoroscopic x-ray series. (b) 50 mSv of skin exposure by an $\alpha$ emitter. (c) 160 mSv of ${\beta }^{–}$ and $\gamma$ rays from the ${}^{\text{40}}\text{K}$ in your body.

How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to $\alpha$ activity?

~2 Gy

What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of $\gamma$ rays?

One half the $\gamma$ rays from ${}^{\text{99m}}\text{Tc}$ are absorbed by a 0.170-mm-thick lead shielding. Half of the $\gamma$ rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these $\gamma$ rays?

1.69 mm

A plumber at a nuclear power plant receives a whole-body dose of 30 mSv in 15 minutes while repairing a crucial valve. Find the radiation-induced yearly risk of death from cancer and the chance of genetic defect from this maximum allowable exposure.

In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of a picometer.

1.24 MeV

Find the mass of ${}^{\text{239}}\text{Pu}$ that has an activity of $\text{1.00 μCi}$ .

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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