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2 Units of Radiation Protection

“All composed things tend to decay.”

Buddha 563–483 B. C.

A large number of units has been proposed and used in the course

of historical development and research in the ﬁeld of radioactivity.

Only those which have survived to today shall be used and deﬁned

here. I will introduce the modern units which are recommended by

the International Commission on Radiological Protection (ICRP).

In addition, I will also mention those units which are still in use

in countries like in the USA, and give the relations to the ICRP-

recommended units used in Europe and elsewhere.

The unit of activity is becquerel (Bq). 1 Bq is one decay per sec-

1 becquerel (Bq) =

1 decay per second ond. The old unit curie (Ci) corresponds to the activity of 1 g of

1 curie (Ci) =3.7×1010 Bq radium-226:1

1 Ci =3.7×1010 Bq ,

1 Bq =27 ×10−12 Ci =27 pCi .(2.1)

In radioactive decays the number of decaying nuclei 1Nis pro-

portional to the number of existing nuclei Nand the observation

time 1t. The number of nuclei decreases by decay. This fact gives

the negative sign for 1N. Therefore, one has

1N∼ −N1t.(2.2)

Since the decay rate changes in time it makes sense to use very

small, indeed inﬁnitesimal times dtand numbers dN(see Appendix

Q),

dN∼ −Ndt.(2.3)

Starting from this relation one obtains the equation by introducing a

constant of proportionality, namely, the decay constant λ,

decay constant

1Because of the frequently occurring very large and very small numbers

I will use throughout the notation using powers, e.g. 106=1 000 000

and 10−6=0.000 001. A word of caution is in order here: A billion is

in most parts of the world 109while in some parts, e.g. in Germany, a

billion is 1012.

C. Grupen, Introduction to Radiation Protection,

Graduate Texts in Physics, DOI 10.1007/978-3-642-02586-0_2,

© Springer-Verlag Berlin Heidelberg 2010

2. Units of Radiation Protection 5

dN= −λNdt.(2.4)

Such a differential equation can be solved generally by the so-called

exponential function (see Appendix Q):

N=N0e−λt.(2.5)

N0characterizes the number of nuclei existing at time t=0, i.e.

the number of originally existing atomic nuclei. The number e =

2.718 28 ... is the basis of the natural logarithm (see Appendix Q).

Since the exponent of the exponential function has to be without

dimension, the physical unit of the decay constant is second−1. The

decay constant λis related to the lifetime of the radioactive source lifetime

as

λ=1

τ.(2.6)

One has to distinguish the half-life T1/2from the lifetime. The half- half-life

life is the time after which a half of the initially existing atomic

nuclei has decayed. After another half-life a half of the remaining

nuclei will have decayed, so that one is left with only one quarter of

the original nuclei. That means, say, after 10 half-lives, there is still

a fraction of 2−10 nuclei which has not decayed. Because of

N(t=T1/2)=N0

2=N0e−T1/2/τ ,(2.7)

we will get, applying the rules of exponential functions and natural

logarithms as explained in Appendix Q,2

1

2=e−T1/2/τ ,

eT1/2/τ =2,

T1/2/τ =ln 2

or T1/2=τln 2 .(2.8)

The decay constant λof an unstable radioactive nucleus is obtained

as

λ=1

τ=ln 2

T1/2

.(2.9)

The activity Aof a radioactive source characterizes the number of activity

decays per second. Therefore, the activity Ais equal to the change

2The exponential function exand the natural logarithm ln xare operations

which are available on most, even simple, non-scientiﬁc pocket calcula-

tors.

6 2. Units of Radiation Protection

rate 1Nof existing atomic nuclei in the time 1t. Because a de-

creasing number of atomic nuclei represents a positive activity, one

deﬁnes

A= − 1N

1t.(2.10)

For inﬁnitesimal time intervals dtone has

A= − dN

dt.(2.11)

With the help of Eq. (2.5) and the rules of calculus as presented in

Appendix Q one obtains:

A= − d

dt(N0e−λt)=λN0e−λt=λN=1

τN.(2.12)

Radioactive sources with a large lifetime τ(or, equivalently,

half-life T1/2) naturally have lower activities if a given number of

nuclei is considered.

The activity in Bq does not say very much about possible bi-

ological effects. These are related to the deposited energy by the

radioactive source in matter. The energy dose D(absorbed energy

energy dose

“I rather stick to the old activity unit.

‘Micro-curie’ sounds so much better

than ‘mega-becquerel’!”

c

°by Claus Grupen

2. Units of Radiation Protection 7

1Wper mass unit 1m),

D=1W

1m=1

ρ

1W

1V(2.13)

(ρ– density, 1V– volume element3), is measured in gray: gray

1 gray (Gy) =1 joule (J) / 1 kilogram (kg) . (2.14)

Gray is related to the old unit rad (radiation absorbed dose, 1 rad =

100 erg/g; still in use in the US) according to:41 Gy =1 J/1 kg

1 Gy =100 rad

1 Gy =100 rad .(2.15)

For indirectly ionizing radiation (i.e. photons and neutrons, but not

electrons and other charged particles) a further quantity character-

izing the energy dose, the ‘kerma’, is deﬁned. Kerma is an abbre- kerma

viation for “kinetic energy released per unit mass”.5The kerma k

is deﬁned as the sum of the initial energies of all charged particles,

1E, liberated in a volume element 1Vby indirectly ionizing radi-

ation divided by the mass 1mof this volume element:

k=1E

1m=1

ρ

1E

1V,(2.16)

where ρis the density of the absorbing material.

We see that kerma relates only to the energy transferred to the

charged particles: it does not depend on which fraction of the ener-

gies of the charged particles is transported out of the volume by par-

ticle motion or by bremsstrahlung. Therefore, kerma is sometimes dose unit of the ﬁrst

interaction step

also called dose unit of the ﬁrst interaction step. The unit of kerma

is also gray (Gy).

Gray and rad describe the pure physical energy absorption.

These units cannot easily be translated into the biological effect of

radiation. Electrons, for example, ionize relatively weakly while,

in contrast, αrays are characterized by a high ionization density.

Therefore, biological repair mechanisms cannot be very effective in

the latter case. The relative biological effectiveness (RBE) depends relative biological

effectiveness

on the type of radiation, the radiation energy, the temporal distribu-

tion of the dose, and other quantities. The relative biological effec-

tiveness is a factor by which we have to multiply the energy dose D

3A volume element, sometimes also called ‘unit volume’, is the differ-

ential element 1Vwhose volume integral over some range in a given

coordinate system gives the total volume V.

41 joule (J)=1 watt second (W s)=1kg m2

s2=107g cm2

s2=107erg

5Occasionally one also ﬁnds “kinetic energy released in matter (or: in

material)”.

8 2. Units of Radiation Protection

of our chosen type of radiation giving the energy dose Dγof X rays

or γrays which would have the same biological effect,

RBE =Dγ/D.(2.17)

Since it is not always known in radiation protection which bio-

logical effects one has to refer to in a speciﬁc case, instead of the

complicated energy-, radiation-, and dose-rate-dependent RBE fac-

tors one uses the so-called quality factor Qto assess the effect of a

physical energy deposition. This leads to the dose equivalent H,dose equivalent

H=Q f D .(2.18)

His measured in sievert (Sv). The factor fconsiders further

sievert

radiation-relevant factors such as the dose-rate dependence or re-

duced biological effects by a periodic irradiation. Such a technique

of intermittent radiation is used in cancer therapy: if a patient should

receive, say, a dose of 2 Sv to destroy a tumor, this dose is applied

e.g. in ten separate fractions of 0.2 Sv, because in the intervals be-

tween these fractions the healthy tissue will recover more easily in

contrast to the tumor tissue. A typical interval between subsequent

fractions of irradiations is a day. All in all the product of the quality

factor Qand the modifying factor fassesses the biological radia-

tion effect of an absorbed dose D. Therefore, this product q=Q f

is called the weighting factor. Since both the quality factor Qandweighting factor

the correction factor fare dimensionless, so is the weighting factor

q, and the unit of the equivalent dose is also J/kg.6The old unit rem

(roentgen equivalent man), still in use in the United States, is related

to sievert according to1 Sv =100 rem

1 Sv =100 rem .(2.19)

Nowadays the weighting factors qare called radiation weighting

factors following a recommendation by the International Commis-

sion on Radiological Protection. These radiation weighting factors

wRdepend on the type of radiation and for neutrons also on their

radiation weighting factors

energy. The most recent deﬁnition of radiation weighting factors

following the recommendation of the International Commission on

Radiological Protection is given in Table 2.1.

For the radiation ﬁeld Rone gets the dose equivalent HRfrom

the energy dose DRaccording to

6The energy dose Dis measured in Gy and the equivalent dose Hin Sv,

therefore, the weighting factor qin principle has the unit Sv/Gy. How-

ever, both Gy and Sv have the same physical unit J/kg, where Gy only

considers the physical effect while Sv also takes the biological effect into

account.

2. Units of Radiation Protection 9

“Atomic progress is quite educating!”

after Jupp Wolter

Table 2.1

Radiation weighting factors wR7

type of radiation and energy range radiation

weighting factor wR

photons, all energies 1

electrons and muons8, all energies 1

neutrons En<10 keV 5

neutrons 10 keV ≤En≤100 keV 10

neutrons 100 keV <En≤2 MeV 20

neutrons 2 MeV <En≤20 MeV 10

neutrons with En>20 MeV 5

protons, except recoil protons, E>2 MeV 5

αparticles, ﬁssion fragments, heavy nuclei 20

HR=wRDR.(2.20)

Figure 2.1 shows photographic records taken with a diffusion cloud

chamber in normal air. They clearly demonstrate the strong ionizing

effect of αparticles from the radon decay chain (left). At the same

time the weakly ionizing effect of decay electrons is visible. Their

tracks in the diffusion cloud chamber are characterized by multiple

scattering and large bending angles (right image).

Apart from these units another quantity is used for the amount of

created charge, the roentgen (R). One roentgen is that radiation dose roentgen

of X rays and γrays, which liberates one electrostatic charge unit

7The energy-dependent radiation weighting factor for neutrons can be ap-

proximated by the function wR=5+17 e−1

6(ln(2En))2, where the neu-

tron energy Enis measured in MeV.

8Muons are short-lived elementary particles which are produced predom-

inantly in cosmic radiation (see also Sect. 11.1).

10 2. Units of Radiation Protection

Figure 2.1

Tracks of αparticles and electrons

in a diffusion cloud chamber

exposed to normal air in buildings.

The different lengths and widths of

α-particle tracks (left image)

originate from projection effects

of electrons and one of ions in 1 cm3of air (at standard temperature

and pressure).

If the unit roentgen is expressed by the ion dose Iin coulomb/kg,

ion dose

one obtains

1 R =2.58 ×10−4C/kg .(2.21)

The tissue equivalent of roentgen is given by

1 R =0.88 rad =8.8 mGy .(2.22)

For an approximate estimate of body doses for photon radiation it is

generally sufﬁcient to work out the photon equivalent dose accord-

ing to

HX=ηIS,(2.23)

where ISis the standard ion dose in roentgen and the scale factor is

scale factor

given by

η=38.8 Sv (C/kg)−1=0.01 Sv/R.(2.24)

To consider the time dependence of the dose equivalent or ion

dose, we use the dose rate. The energy-dose rate is the change of

dose rate

the energy dose 1Din the time 1t. Since the dose rate changes

rapidly, particularly for radioactive sources with short half-life, it is

advisable to use the differential notation (see Appendix Q). Depend-

ing on whether one prefers the notation ( d

dt) introduced by Leibniz

or the notation favored by Newton, as characterized by a dot over

the quantity, one writes for the energy-dose rate

dD

dtor,equivalently,˙

D.(2.25)

Correspondingly, also the dose-equivalent rate is given by

dose-equivalent rate

dH

dt≡˙

H(2.26)

2. Units of Radiation Protection 11

and the ion-dose rate by ion-dose rate

dI

dt≡˙

I.(2.27)

The physical units of these quantities are:

[˙

D] = J

kg s =W s

kg s =W

kg ,(2.28)

[˙

H] = [ ˙

D],(2.29)

[˙

I] = C

kg s =A s

kg s =A

kg .(2.30)

˙

Dand ˙

Hare therefore measured in watt per kilogram and ˙

Iin am-

pere per kg.

The received dose can be related to the whole body (whole-body whole-body and partial-body

dose

dose) or also only to speciﬁc parts of the body (partial-body dose).

The dose equivalent that has accumulated within 50 years after a

single incorporation9of radioactive substances in a certain organ or

tissue is called ‘50-years dose-equivalent commitment’. 50-years dose-equivalent

commitment

If a radiation exposure with an average per capita dose-equiva-

lent rate ˙

H(t)for a population group over an extended period has

occurred, a dose-equivalent commitment is deﬁned by dose-equivalent commitment

Hf=X˙

H(t) 1t,(2.31)

where one has to sum over the relevant time intervals 1t. If this dose

rate ˙

H(t)does not depend on the time, one has

Hf=˙

H t ,(2.32)

where tis the considered time interval.

The collective dose is the product of the total number of persons collective dose

Nby one person’s average dose hHiin sievert or, more generally,

the collective equivalent dose Sis

S=X

k

PkhHki,(2.33)

9When radioactive substances enter the human body, the radiation effects

are different from those resulting from exposure to an external radiation

source. Especially in the case of alpha radiation, which has a rather short

range and normally never penetrates the skin, the exposure can be much

more damaging after ingestion or inhalation. The terms ingestion and

inhalation and the intake of radioactive compounds through wounds after

accidents are usually subsumed under the expression incorporation.

12 2. Units of Radiation Protection

Table 2.2

Tissue weighting factors wT

organ or tissue tissue weighting factor wT

gonads 0.20

red bone marrow 0.12

colon 0.12

lung 0.12

stomach 0.12

bladder 0.05

chest 0.05

liver 0.05

esophagus 0.05

thyroid gland 0.05

skin 0.01

periosteum (bone surface) 0.01

other organs or tissue 0.05

where hHkiis the per capita equivalent dose in an interval Hk...

Hk+1Hkand Pkthe number of persons with radiation exposures

in this interval.

In many cases it is necessary to convert a partial-body dose into

a whole-body dose. Therefore, a weighting factor wThas to be at-

tributed to the irradiated organs of the body. This effective dose

effective dose equivalent

equivalent is deﬁned as

Heff =

n

X

T=1

wTHT,(2.34)

where HTis the average dose equivalent in the irradiated organ or

tissue and wTis the weighting factor for the Tth organ or tissue.10

For the purpose of radiation protection it is simply deﬁned that

the human has thirteen ‘organs’. The weighting factors are normal-

tissue weighting factor

ized to 1 (Pwi=1). These tissue weighting factors are compiled

in Table 2.2.

It is assumed that the inhomogeneous irradiation of the body

with an effective dose equivalent Heff bears the same radiation riskradiation risk

as a homogeneous whole-body irradiation with H=Heff.

The determination of the dose-equivalent rate by a pointlike ra-

diation source of activity Acan be accomplished using the following

formula:

˙

H=ΓA

r2.(2.35)

In this equation ris the distance from the radiation source (in me-

ters) and Γa speciﬁc radiation constant which depends on the type

and energy of the radiation. For βrays additionally the traveling

10 In some cases the effective dose equivalent Heff is also denoted with E

in order to stress that in this case we are dealing with an effective dose.

2. Units of Radiation Protection 13

Table 2.3

Dose constants Γfor some β- and

γ-ray emitters11

radioisotope βdose constant

³Sv m2

Bq h ´

32

15P 9.05 ×10−12

60

27Co 2.62 ×10−11

90

38Sr 2.00 ×10−11

131

53I 1.73 ×10−11

204

81Tl 1.30 ×10−11

radioisotope γdose constant

³Sv m2

Bq h ´

41

18Ar 1.73 ×10−13

60

27Co 3.41 ×10−13

85

36Kr 3.14 ×10−16

131

53I 5.51 ×10−14

133

54Xe 3.68 ×10−15

137

55Cs 8.46 ×10−14

distance of electrons has to be considered. Table 2.3 lists the βand

γdose constants for some commonly used radiation sources. The dose constant

1/r2dependence of the dose-equivalent rate is easily understood, if

one considers that for isotropic emission (i.e. equally in all direc-

tions) the irradiated area for larger distances increases quadratically

with distance r. The radiation emerging from the source has to pass

through the surface of the virtual sphere (surface of sphere =4πr2),

consequently the radiation intensity per unit area decreases like 1/r21/r2law

(‘solid-angle effect’).

The differences in the βand γdose constants originate from

the fact that electrons will normally deposit all of their energy in

the body while the absorption power of the body for γrays is energy absorption

much smaller. Differences in the βor γdose constants for differ-

ent radioisotopes have their origin in the different energy of the

11 A chemical element is characterized by the number of positively charged

nucleons (i.e. protons, with proton number =Z). Furthermore there are

neutrons in the atomic nucleus which are essential for the binding of

nuclei (neutron number =N). The atomic mass Ais given by the sum

of the proton and neutron numbers Z+N. Nuclei with ﬁxed proton

number but variable neutron number are called isotopes of the element

with the atomic number Z. Isotopes which are radioactive are called

radioisotopes. An isotope is characterized by the number of protons Z

and neutrons Nusing the notation A

ZElement. Since the name of the ele-

ment is uniquely determined by Z, this index is frequently omitted, e.g.

137

55Cesium or 137 Cesium.

14 2. Units of Radiation Protection

© by Claus Grupen

emitted βand γrays. As an example 137Cs radiates a photon of

energy 662 keV and 60 Co two γrays with energies 1.17 MeV and

1.33 MeV. Consequently the γdose constant for 60 Co is larger than

for 137Cs, even though the absorption coefﬁcient for MeV photons

is somewhat smaller compared to 662-keV photons.

A pointlike 137Cs γ-ray emitter of activity 10 MBq produces a

dose-equivalent rate of 0.846 µSv/h at a distance of 1m. A 60Co

source of the same activity leads to a dose-equivalent rate of 3.41

µSv/h at the same distance. The dose-rate ratio of these two sources

dose-rate ratio

corresponds roughly to the ratio of the deposited energies.

2.1 Supplementary Information

A radiation ofﬁcer detects a contamination with 131I in a medicalExample 1

contamination laboratory which leads to an ambient-dose rate of 1 mSv/h. He de-

ambient-dose rate cides to seal the room and wait until the activity due to the iodine

contamination has decayed to such a level that the ambient-dose rate

is only 1 µSv/h. For how long has the room to be sealed?

The half-life of the 131I isotope is 8 days. The dose rate and

consequently the activity should be reduced by a factor of 1000.

The decay law

N=N0e−t/τ

leads to a time dependence of the activity Alike

decay time constant

2.1 Supplementary Information 15

A=A0e−t/τ ,

where A0is the initial activity. With A/A0=10−3and τ=

T1/2/ln 2 one has

exp µ−tln 2

T1/2¶=10−3

and

t=¡T1/2/ln 2¢ln 1000 =79.7 days .

Consequently about 10 half-lives ((1/2)10 =1/1024) are required

to reach the necessary reduction factor.

A historical example for the speciﬁc activity leads to the deﬁnition Example 2

speciﬁc activity

of the old unit curie:

The half-life of 226Ra is 1600 years. This leads to the speciﬁc

activity (i.e. the activity per gram) of:

A∗=λN=ln 2

T1/2

NA

MRa

=ln 2

1600 yr

6.022 ×1023

226

=3.7×1010 Bq =1 curie .

(NAis the Avogadro constant and MRa the atomic weight of 226 Ra-

dium, 1 yr =3.1536 ×107s.)

The radiation units presented so far have been recommended by the Example 3

International Commission on Radiological Protection (ICRP). In ad-

dition, also the International Commission on Radiation Units and

Measurement (ICRU) has proposed a slightly modiﬁed concept of modiﬁed dose quantities

dose quantities in the ﬁeld of radiation protection. These quantities

differ from the units presented so far by higher specialization and

stronger formalization. These specialized dosimetric units are fre-

quently used in national radiation-protection regulations.

If in a speciﬁc tissue, organ, or part of the body, T, the energy

dose DT,Ris caused by a radiation ﬁeld of type R, then the equiva- radiation ﬁeld

lent or organ dose is obtained by using the radiation weighting factor

wRas follows:

HT,R=wRDT,R,(2.36)

where wRis the radiation weighting factor given in Table 2.1.

Equation (2.36) deﬁnes the partial-body doses Tfor a given ra-

diation ﬁeld R. If several different types of radiation (α,β,γ,n)radiation quality

work together, the corresponding partial-body dose is given by

HT=X

R

HT,R=X

R

wRDT,R.(2.37)

16 2. Units of Radiation Protection

The effective dose equivalent Heff =Ecan be derived from Eq.

(2.37) by weighting the different energy doses with the tissue weight-

ing factors wT, which have been presented in Table 2.2:

E=Heff =X

T

wTHT=X

T

wTX

R

wRDT,R.(2.38)

Furthermore, dose units for penetrating external radiation (deposit-

ing most of their energy in the ﬁrst 10 mm of tissue) and for radiation

of low penetration depth (70 µm skin depth) have been introduced in

many national radiation-protection regulations. In personal dosime-

operative units

of personal dosimetry try these operative units are denoted with Hp(10),Hp(0.07).

In the past these operative units had been determined with ﬁlm

badges (see Sect. 5.6). However, the measurement of the depth doses

Hp(10)and Hp(0.07)with ﬁlm badges is not very accurate. A pre-

depth dose

cise value for the skin dose as derived from the penetration depth

of the radiation can be obtained with more sophisticated dosimeters.

Such a new type of dosimeter, called ‘sliding-shadow’ dosimeter,

has been developed, which allows a reliable determination of the

skin doses.12 These dosimeters are optimized for a depth-dose de-

‘sliding-shadow’ method

termination and allow at the same time a determination of energy

and angle of incidence of photons, and they can further discriminate

between βand γrays.

The availability of this new measurement technique necessitated

to convert the hitherto existing quantities Hp(10)and Hp(0.07)into

the new quantities H∗(10)and H∗(0.07). The conversion factors

depend on the photon energy and the angle of incidence. For en-

vironmental radiation, γrays or X rays from X-ray tubes with ac-

celerating voltages below 50 kV and above 400 kV the conversion

factor is 1; i.e. the old and new depth doses are identical. For γ

conversion factor

for depth doses rays from radioactive sources which are frequently used as X-ray

sources (e.g. 57Co, 67 Ga, 75Se, 99mTc, 153 Gd, 153Sm, 169Yb, 170Tm,

186Re, 192 Ir, 197Hg, 199Au, 201 Tl, 241Am) and for the radiation ﬁeld

of X-ray tubes operated with accelerating voltages between 50 kV

and 400 kV, the conversion factors are H∗(10)/Hp(10)=1.3 and

H∗(0.07)/Hp(0.07)=1.3. This means that the depth doses as de-

termined with the old ﬁlm badges have to be increased by 30%.

More details on the new skin doses can be found in the article

“New quantities in radiation protection and conversion coefﬁcients”

12 These ‘sliding-shadow’ dosimeters use a special arrangement of struc-

tured metal and plastic ﬁlters and directional indicators. In addition, β

rays can be distinguished from γrays, which is essential for a reliable

individual depth-dose information. The different absorption coefﬁcients

of the ﬁlters used allow an accurate measurement of the skin dose over a

wide energy range. The basic detector behind the arrangement of ﬁlters

is still a sensitive ﬁlm, like in the old ﬁlm badge.

2.1 Supplementary Information 17

Proposal for a new unit for radiation protection

The common units for radiation doses (Gy, Sv) are not very persuasive for a broader audience. The layman

also has difﬁculties to interpret a dose given in Gy or Sv. Even relatively low radiation exposures which can

only be detected because of extraordinarily sensitive measurement devices (one can measure the decay of

individual atomic nuclei without difﬁculty) occasionally lead to over-reactions in public discussions. It is,

however, very important to express radiation levels, caused, for example, by CASTOR transports or nuclear

power plants, in units which can be understood and interpreted by the layman. It is perfectly sufﬁcient to

appreciate the order of magnitude of a radiation exposure, i.e., in easily comprehensible and self-explaining

units which can be judged upon intuitively.

Mankind has developed with permanent natural radiation caused by cosmic rays and terrestrial rays and by

permanent incorporation by ingestion and inhalation of natural radioisotopes. There are no hints whatsoever

that this radiation has created any biological defect, it may even have increased the biodiversity. The natural

radiation dose is subject to regional variations, but the natural annual radiation dose does not fall below

2 mSv for anybody. This natural annual dose sets the scale on which to judge on additional radiation burdens

by civilization, for example, by medical diagnosis.

It is therefore proposed to use this typical value of the inevitable annual dose (IAD) due to natural radiation

as a scale against which additional radiation exposures should be judged in discussions in the public:13

1 IAD =2 mSv .

In these units the following table gives some typical radiation exposures.

type of radiation exposure dose in IAD

X-ray of a tooth 0.005

radiation level by nuclear power plants ≤0.01/yr

CASTOR transport for accompanying persons ≤0.015

air ﬂight London – New York 0.015

X-ray of the chest 0.05

mammography 0.25

scintigraphy of the thyroid gland 0.40

heavy smoker (more than 20 cigarettes per day) 0.50/yr

positron-emission tomography 4.0

computer tomography of the chest 5.0

limit for radiation-exposed persons in Europe 10

limit for radiation-exposed persons in the USA 25

maximum life dose for radiation-exposed persons in Europe 200

lethal dose 2000

local cancer therapy ≈30 000

Based on these numbers everybody can judge independently on the realistic risk caused by radiation

exposures.

13 G. Charpak and R. L. Garwin proposed a similar unit; they set the scale by the body-intrinsic radioactivity

which leads to an annual radiation dose of 0.2 mSv. They named this dose 1 DARI, where the acronym DARI

stands for Dose Annuelle due aux Radiations Internes. Europhysics News 33/1, p. 14 (2002).

18 2. Units of Radiation Protection

published by the British Committee on Radiation Units and Mea-

surements (see also J. Soc. Radiol. Prot. Vol. 6, p. 131–136, (1986)).

Summary

The essential units of radiation protection are becquerel (Bq) for

the activity, gray (Gy) for the purely physical energy deposi-

tion per mass unit, and sievert (Sv) for the energy dose weighted

by the biological effectiveness. A further characteristic quantity

for a radioactive isotope is its half-life T1/2. Radioisotopes with

large half-lives are associated with a low activity, and those with

short half-lives with a high one. The activity alone is not a good

measure for a possible biological damage. This damage depends

on the type of emitter and, of course, on the distance to the radi-

ation source.

2.2 Problems

A radioactive material possesses an approximately constant gammaProblem 1

activity of 1 GBq. Per decay 1.5MeV are liberated. What is the daily

energy dose if the ionizing radiation is absorbed in an amount of

material of mass m=10 kg?

In a nuclear physics laboratory a researcher has inhaled dust of aProblem 2

90Sr isotope by accident, which has lead to a dose rate of 1 µSv/h

in his body. The physical half-life of 90Sr is 28.5 yrs, the biological

half-life for retention in the lung (see Chap. 13, Page 217) is only

80 days. How long does it take until the dose rate has decreased to

0.1µSv/h?

(The biological half-life is deﬁned by the time until 50% of the ac-

tivity is eliminated by the body by normal biological activity.)

At a distance of 2 m from a pointlike 60Co source a dose rate ofProblem 3

100 µSv/h is measured. What is the activity of the source?

(To solve this problem you should use information from Figs. 3.4

and 4.4.)

The radioisotope technetium 99m is frequently used in nuclear med-Problem 4

nuclear medicine icine. 99mTc is a metastable state of 99 Tc, it has a half-life of 6 h.

What kind of activity has a patient who was administered an activity

of 10 MBq 99m Tc for a kidney examination after a period of two

days? For this estimate one can assume that the effective half-life

can be approximated by the physical half-life.