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Dose in rem is defined by 1 rad = 0 . 01 J/kg size 12{"1 rad"` \( r \) =0 "." "01"`"J/k"} {} and rem = rad × 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.


The activity R = 1 . 00 μCi = 3 . 70 × 10 4 Bq = 3 . 70 × 10 4 size 12{R=1 "." "00"`"μCi "=" 3" "." "70" times "10" rSup { size 8{4} } `"Bq"=3 "." "70" times "10" rSup { size 8{4} } } {} decays/s. So, the number of decays per year is obtained by multiplying by the number of seconds in a year:

3 . 70 × 10 4 decays/s 3 . 16 × 10 7 s = 1 . 17 × 10 12 decays.

Thus, the ionizing energy deposited per year is

E = 1 . 17 × 10 12 decays 5 . 23 MeV/decay × 1.60 × 10 13 J MeV = 0 . 978 J.

Dividing by the mass of the affected tissue gives

E mass = 0 . 978 J 2 . 00 kg = 0 . 489 J/kg. size 12{ { {E} over {"mass"} } = { {0 "." "978" `J} over {2 "." "00"`"kg"} } =0 "." "489"`"J/kg."} {}

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

dose in Gy = 0.489 J/kg 1.00 (J/kg)/Gy = 0.489 Gy.

Now, the dose in Sv is

dose  in  Sv = Gy × RBE size 12{"dose"`"in"`"Sv"=" Gy " times " RBE"} {}
= 0.489 Gy 20 = 9.8 Sv. size 12{ {}= left (0 "." "49"`"Gy" right ) left ("20" right )="10"`" Sv."} {}


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 α emitter makes the effects 10 to 20 times worse than the same ionization produced by β s, γ rays, or x-rays. An activity of 1.00 μ Ci is created by only 16 μ g of 239 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 131 I size 12{"" lSup { size 8{"131"} } I} {} . Because of its relatively long half-life, it exposes the thyroid to about 0.75 Sv. The isotope 123 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.

Alpha Decay

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 = 0.01 J/kg . size 12{1`r=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
    rem = rad × RBE . size 12{"rem"="rad" times "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
    Sv = Gy × RBE  and 1 Sv = 1 00 rem.
  • 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 10 / 10 6 rem·y size 12{"10"/"10" rSup { size 8{6} } } {} 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 α radiation are relatively safe outside the body and exceptionally hazardous inside. Yet those that emit γ size 12{γ} {} radiation are hazardous outside and inside. Explain why.

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

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

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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?


Figure A shows a “shoe fitting x-ray device.” Figure B shows a group of people wearing white protective suits standing near a yellow radiation hazard sign.
(a) This x-ray fluorescence machine is one of the thousands used in shoe stores to produce images of feet as a check on the fit of shoes. They are unshielded and remain on as long as the feet are in them, producing doses much greater than medical images. Children were fascinated with them. These machines were used in shoe stores until laws preventing such unwarranted radiation exposure were enacted in the 1950s. (credit: Andrew Kuchling ) (b) Now that we know the effects of exposure to radioactive material, safety is a priority. (credit: U.S. Navy)

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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.)

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

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

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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 α exposure?

(a) 100 mSv

(b) 80 mSv

(c) ~30 mSv

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Find the radiation dose in Gy for: (a) A 10-mSv fluoroscopic x-ray series. (b) 50 mSv of skin exposure by an α emitter. (c) 160 mSv of β and γ size 12{γ} {} rays from the 40 K size 12{"" lSup { size 8{"40"} } K} {} in your body.

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

~2 Gy

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What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of γ size 12{γ} {} rays?

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One half the γ rays from 99m Tc size 12{"" lSup { size 8{"99m"} } "Tc"} {} are absorbed by a 0.170-mm-thick lead shielding. Half of the γ 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 γ rays?

1.69 mm

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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.

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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

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Find the mass of 239 Pu that has an activity of 1.00 μCi .

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