<< Chapter < Page Chapter >> Page >

Strategy

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.

Solution

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."} {}

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 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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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)

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)

Got questions? Get instant answers now!

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.)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 α exposure?

(a) 100 mSv

(b) 80 mSv

(c) ~30 mSv

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

what is circut
hasiya Reply
newtons law of motion
hasiya
First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
Manan
is the ability to do work
Adjah Reply
what is energy
Mercy Reply
energy is ability of the capacity to doing work
shafiu
what is vector
mosco Reply
A quantity that has both magnitude and direction
Donaldo
can a body with out mass float in space
mosco
Is the quantity that has both magnitude and direction
Amoah
Yes it can float in space,e.g.polyethene has no mass that's why it can float in space
Amoah
that's my suggestion,any other explanation can be given also,thanks
Amoah
A charge of 1.6*10^-6C is placed in a uniform electric field in a density 2*5^10Nc^-1, what is the magnitude of the electric force exerted on the charge?
Omotosho Reply
what's phenomena
Enoch Reply
Phenomena is an observable fact or event.
Love
Prove that 1/d+1/v=1/f
James Reply
What interference
Moyinoluwa Reply
What is a polarized light called?
Moyinoluwa
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
what's velocity
mosco
Velocity is the rate of change of displacement
Divya
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask