H. M. Parker
This document consists of 8 pages.
Date of Manuscript:
May 28, 1947
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RADIATION HAZARDS OF BREMSSTRAHLUNG
By H. M. Parker
been caused to radiation workers by bremsstrahlung (continuous
X-ray spectrum) than by any other type of radiation. This report is concerned not at all with hazards
associated with general x radiation, but only with the bremsstrahlung arising from the beta radiation
of pile produced activities (either fission products or induced radioactivites).
For convenience, bremsstrahlung will henceforth be anglicized to BS. It is evident, a priori, that
the BS will rarely be the major factor in a radiation exposure and some apologia for this investigation
1) This secUtion is currently attempting to reconcile the observed gamma radiation from a large
tank of liquid with the theoretical estimate. BS may be a correction factor comparable with the total
uncertainty and its magnitude must be determined.
2) T. H. Davies recently pointed out that solution in the new separations process show a re-
markably high ratio of 3 to -, activity. In one case. about 100 curies of 3 activity were associated with
I curie of > activity. Special attention to the BS from a large mass of material may be required.
2) Brief mention of BS from tanks in the Project literature refers to the radiation from the metal
wall as the possible hazard. It seemed more likely that the radiation in the liquid would be greater.
4) In this laboratory there has been considerable misconception about the choice of container for
3 emitter, whether a glass bottle containing
such an emitter
should be contained in an alu-
minum lined shield. etc.
rt attempts to settle these four points.
RADIATIVE ENERGY LOSS OF AN ELECTRON
that of Heitler's Quantum Theory of
= electron energy, units
= electron mass
c = velocity of light
section for radiative energy loss,
= number of atoms (molecules) per cmn, Z nuclear charge
= total number of electrons per cm'
- sum of Z2 of all nuclei per cm3
1 Mev will be considered equal to 2 mce
By and large, more damage has
BS IN LEAD: TOTAL ENERGY
Total energy loss per cm ( tot
The radiation loss -drd = NE
is given by Heitler on pages 221 and 222.
rad .. (equation 220) can be computed from page 143.
The fractional energy loss by electrons of different energy in lead is given in Table 1.
The energy converted into BS by the complete stopping of a 5 mc2 particle will be less than that
obtained by the summation of the separate losses in Table 1. This upper limit will be taken as the
total energy loss.
BS IN LEAD: ENERGY DISTRIBUTION
Heitler considers the continuous spectral distribution on pages 168 to 171. From these data the
energy loss over the energy steps of Table 1 had been calculated by dividing the appropriate BS spec-
trum into energy intervals of 0.4 me2
. Accuracy cannot be claimed for these spectra. Table 3 gives
the spectral energy for successive energy losses of 1 mc2. The table
is useful for calculations wherein
an electron traverses a thin metal sheet and loses only part of its energy. Table 4 was derived from
Table 3 by summation. These are the figures required in this report, corresponding to complete stop-
page of the electron in the medium.
BS IN OTHER MEDIA
The energy loss due to collisions is very nearly proportional to (NZ
is proportional to (NZ2). Hence, the radiative loss in media other than lead can be written down. It
can be assumed that the spectral distribution will be the same in all
The radiative energy loss
Table 5 gives a few values of energy loss in convenient media for 2 Mev particles. The ratio of
values for any two substances will be the same at other energies.
Table 1. Energy loss of an electron in lead.
loss by BS
Table 2. Total BS by an electron in lead.
Mev .25 .5 1 1.5 2 2.5
Table 3. Spectral distribution of BS (in Pb) over different energy intervals.
BS energy me2
BS energy interval
BS spectral energy mc2 x 10O
Table 4. Total spectral distribution of BS (in Pb) for given primary electron energy.
BS energy Mev
BS energy in Key
Total 43.6 97.4 172.0 262.7
Table 5. Fractional energy loss of 2 Mev particle as BS.
Material Fractional Material Fractional
energy loss energy loss
HO .0136 20% UNH .0291
Pyrex glass .0214 Fe .0512
Common glass .0232 Pb .147
BS FROM TANKS OF RADIOACTIVE LIQUID
For simplicity, cylindrical tanks will be considered with the observer on the axis produced. The
absorbing wall of the tank
is then a flat plate.
BS FROM AN INFINITELY LARGE TANK OF LIQUID
If Em = energy of BS in the interval of average energy in Mev
gm = linear absorption coefficient of liquid for m Mev radiation
= scattering absorption coefficient of m Mev radiation in air.*
The ionizatiun outside a large tank of liquid containing a P emitter only
The magnitude of the BS
per cc with 1 curie of 2
y,("as)m Em .or -
x S (aa) Em (equation 310) taken over all values of m.
conveniently shown by comparing the effect of 1 curie of 2 Mev 3 activity
Mev v activity.
are given in Table 6. The BS considered here is from the liquid only. The fil-
tration of the postulated tank walls
is computed by applying factors F,(gm d), since the absorption oc-
curs through an indefinitely extended sheet, thickness d. It
is clear that the BS does not vary radically
with the composition of the liquid. For all practical purposes, figures for 20% UNH solution will apply
well enough to any solution in the separation process. With a normal tank wall of about 3 mm Fe, n150
Mev p will give total gamma activity equivalent to 1 curie of
2 Mev y. This answers I(1)
and indicates that 1(2) may just become of some significance.
Table 6. BS from large tanks.
Liquid HzO equiv. 20% UNH Pb
Tank wall 0 5 mm Pb '0 3 mm Fe 5 mm Pb 10 mm Fe 0 5 mm Pb
Energy M I x 107 I x 107 I I I I I x 107 I x 107
.1 Mev 9.0 12.5 2.0 .1 .3 -
.3 10.5 .2 11.2 5.6- .2 1.9 2.6 .05
.5 9.5 1.4 14.6 8.2 2.2 3.2 4.8 .7
.7 7.9 2.3 14.3 8.6 4.2 3.9 6.2 1.8
.9 6.3 2.2 11.2 7.1 4.0 3.4 5.5 2.0
1.1 4.5 1.7 7.9 5.1 3.2 2.6 4.3 1.7
1.3 3.5 1.4 6.3 4.2 2.7 2.3 3.4 1.5
1.5 2.0 1.0 3.8 2.7 1.7 1.5 2.0 .9
1.7 1.4 .7 2.6 1.8 1.2 1.0 1.4 .7
1.9 .7 .4 1.3 .9 .7 .6 .7 .4
Total 55.3 11.3 85.7 46.2 20.1 20.5 26.2 9.8
2 Mev y 12100 6600 10200 7300 5600 4400 1100 600
equiv. to 219 583 119 157 278 214 42 61
1 curie y
* (a + 7)
is used for low energy where the photoelectric absorption is significant.
BS FROM A TANK WALL
Consider the number of particles incident on a plane wall
from a liquid emitting n particles/cmr/sec. Number Incident
on unit area from volume element dV is
dN= nd cos 4 (410)
= angle between normal and direction of element dV.
= distance to element dV
= azimuthal angle
where R is the range.
Equation 410 agrees with the convenient approximation that of all electrons emitted within the
range thickness R, one-half approach the wall, and of them one-half again will fail to reach the wall
because of obliquity.
It has been shown previously (CH930) that the average energy of p particles reaching a surface
Hinder these conditions is 0.6 x primary energy. As the higher energies are emphasized in the BS one
can reasonably take 1.5 Mev as the effective energy of electrons impinging on the wall from 2 Mev
particles in the liquid.
BS FROM AN INFINITE STEEL WALL THICKNESS t
The radiation from an indefinitely large sheet of thickness t, when the far side is a BS emitter
due to electrons impinging on it is
= Const x Z (oa) m Em Fo (pm t)
It is assumed provisionally that the energy Em is radiated uniformly in all directions. Table 7 gives
values for the BS in steel walls with 20% UNH solution. This method of calculation will give poor
values for great wall thicknesses because no BS harder than 1.5 Mev has been allowed. Calculations
with the full 2 Mev energy and the present thickness give results about twice as great.
Table 7. BS from steel tank wall. 20% UNH solution.
3 mm Fe wall
10 mm Fe wall
aoE x 18
2 Mev y in liquid
Curies of 8 equivalent
to 1 curie y in liquid
67.3 x 10'
4.4 x 104
it is certain that the wall effect
is much less than'that from the liquid.
For 3 mm Fe wall, I wall/I liquid = .054
For 10 mm Fe wall, I wall/I liquid = .035
The other extreme case is that of a deep tank of very small surface area.
In common units
where g and g
liquid e- d
are the absorption coefficients in liquid and wall. For
3 mm Fe I wall/I liquid
10 mm Fe I wall/I liquid
= 0.3 and 139 curies 3:
= .024 and 178 curies p
20% UNH and a steel wall
= 1 curie
= 1 curie y
Neither the ratio of I wall/I liquid nor the curie equivalents have changed much. All other values
for deep tanks will be between these limits.
Shallow tanks could obviously give values of I wall/I liquid greater than these. But for all practi-
Shallow tanks could obviously give values of I wall/I liquid greater than these. But for all practi-
cal purposes a tank 15 cm deep
a "deep tank"
and the shallow tank
need not be considered.
DIRECTIONAL FEATURE OF WALL RADIATION
High energy BS
is confined to the forward direction within a solid angle of
The BS from
the bombarded wall will, therefore, be almost wholly confined to the forward hemisphere. As a rough
correction the wall radiation in 4.2 and 4.3 should be approximately doubled. However, relation (equa-
tion 410) indicates that the incident ( radiation obeys a cosine law. Therefore, the resultant BS will
also be directional.
To maintain the total energy emission constant, the relations shown in Table 8 hold for postulated
Emission law Energy emission at angle Bs from a large plate
Uniform E for t = 0-w I = KE Fo( t)
Cos 4E cos, <, = 0 -*/2 It = 4KE F (p t)
0, < = 7/2 w
Cos2 6E cos <, z= 0--w/2 I1= 6KE F (g t)
0, > /2
Fermi distribution 1.857 E(cos 4 + V3 cos2P) IF = 1.857 Fi -3.217 F2
Cos' 2(n + 1)E cos" n1 = 2(n-1)KE Fn n t)
Some values of these functions are given in Table 9.
For a steel tank 3 mm thick (p t) ranges from 0.1 to 1.0.
If one considers the combination of varying emission law
at different energies with changes in the functions, it can
be seen that a universal factor of 2 would be a good ap-
The BS from the wall is
greater than about 10% of that from the tank in the usual
MAGNITUDE OF THE EFFECTS IN ROENTGENS
It has seemed convenient to use the curie equivalent
method of presentation, namely, to write down the number
jt I/I i/ IF/I
.01 0.941 0.729 0.827
.05 1.342 1.106 1.216
.10 1.586 1.371 1.471
.20 1.879 1.727 1.798
.50 2.334 2.375 2.357
1.0 2.709 3.001 2.866
2.0 3.071 3.698 3.408
5.0 3.478 4.592 4.075
of curries of 2 Mev p activity which gives rise to BS equal in ionizing power to 1 curie of 2 Mev v ac-
tivity under the same conditions.
, To convert BS values to roentgens a series of alleged values for 2 Mev v cases is given in Table
10. The tanks are supposed infinitely deep.
FROM SHIPPING CONTAINERS
The problem here is to decide whether
1) it is necessary to line a container with material of
Jo1 atomic number or (2) whether additional lead shielding should be allowed in either case to cut
mown the BS component in a mixed 3 and y source.
It will be supposed that all particles of primary energy 2 Mev strike the wall with the full energy.
hn some cases this will mean by the argument given in the section, BS from a Tank Wall, that the ef-
feet quoted will be that due to-3 Mev particles.
COMPACT SOURCE IN LEAD OR ALUMINUM
Co insider that all the electrons emitted immediately enter the metal. The resulting BS is shown in
Figure 2 for thickness of lead shield to 10 cm expressed as curie equivalents as before, and also more
conveniently here as me of y activity (2 Mev) per curie p activity. For lead containers there is a pos-
sible radiation hazard. Since a container of less than 1-inch wall is hardly worth consideration, a
Table 10. Gamma radiation from sundry tanks containing 1 curie of 2 Mev v activity per Ce.
Tank wall 0 3mm Fe 10 mm Fe 5 mm Pb
bist. from Tank ---------^--------
tank diameter Dosage rate in kr/hr
1 cm 20 cm 958 751 500 623
1 50 1704 1363 852 1041
1 100 2161 1640 1019 1240
10 20 378 227 166 247
10 50 951 783 575 692
10 100 1328 1221 906 1075
25 20 157 ,81 50 104
25 50 475 356 261 350
25 100 769 869 635 756
S2326 1731 1062 1275
0.3 0.4 0.5
\4 / 1oo
1-----4 _6--1 0 0 0
- --- --- -4 100
1.0 a 3 4 5 67 10
CM Pb SHIELD
convenient rule is that the BS hazard is about 1 me y equivalent per curie 3. If an aluminum liner is
used, the radiation is reduced by a factor of 5 or 6.
EXTENDED SOURCE IN LEAD, ALUMINUM,
In general, a strong source will consist either of a pellet of perhaps 1-inch diameter or of a solu-
tion. In the first case, about one-fifth or less of the 8 particles will expend themselves in the sur-
rounding metal and the remainder in the pellet itself.
The total BS would be about twice
as great in
a lead container
as in an aluminum one and the choice of metal container is not likely to be critical.
The second case is that which arises frequently in the laboratory. A solution is to be shipped in
a glass bottle. A typical bottle is 3.2 cm diameter, 2.65 mm wall thickness, filled to 3 or 4 cm. The
BS is then independent of the outer container
uid or glass.
as the B radiation is essentially all absorbed in the liq-
With no outer shield there will be about 1 me y equivalent per curie B, with shield of
1-inch Pb or more,
0.2 me per curie. Containers for such bottles should not have aluminum liners
as it is uneconomical not to introduce the lead shielding at the smallest possible radius.
UNIVERSITY OF FLORIDA