Memorandum from R. L. Murray to C. K. Beck
Typescript
2 pp.
January 16, 1952
MurNBcoolingwater011652


[page 1]

January 16, 1952

TO: C. K. Beck
FROM: R. L. Murray SUBJECT: ACTIVITY OF REACTOR COOLING WATER
CC: Reactor Committee

In preparation for an earlier reporta, Dr. A. C. Menius computed the induced
activity in reactor cooling water exposed for two seconds in a thermal flux of
1012. These calculations are brought up to date in light of the final decision
on flow rates and cooling coil dimensions, and an independent check provided.

Analysis: A given cubic centimeter of water remains within the core flux for a
time given by
t = l/v/A
where l the path length (7 feet), v is the flow velocity corresponding
to 1 gallon/minute in each of four tubes, and A is the internal cross-section of
the pipe (1/4" I.D.).

Thus,

The rate of formation of radioactive atoms is given by
g = [phi]N[sigma]at
where [phi] is the average thermal flux (5 x 1011), N is the number of target atoms
per unit volume, and [sigma]a is the thermal neutron cross-section,
N = (ppm)(10-6)(0.0335 x 1024)(isotopic abundance).

The activity induced in (d/sec) is [lambda]g or .693g/tH where [lambda] is the decay constant
in sec-l and tH is the half-life in sec.

In the attached table, a conservative assumption of exposure time of 2 seconds
in a flux of 1012 is still used, ie, [phi]t 2 x 1012 cm-2.


[page 2]

Target
Isotope
From
the im-
purity
Pars perb
Million
of Water
Active
iso-
tope
Half-c
life
[lambda](sec-1)[sigma]a ofc
Target
(barns)
Abundancec
of Target
Isotope(%)
N
(cm-3)
Activity
(d/sec)
Si30SiO29.8S312.7h.7.1x10-50.123.11.0x1016.017 .17?
Fe54Fe0.02Fe553y7.3x10-925.93.95x1013neg
Fe58Fe0.02Fe5947d.1.7x10-70.360.342.3x1012neg
Ca44Ca8.7Ca45152d.5.3x10-80.62.16.1x1015neg
Mg26Mg1.4Mg279.58m1.2x10-30.0511.35.3x10150.64
Na23Na+K4.2Na2414.9h1.3x10-50.61001.4x10172.2
C13CO3
HCO3
3.9
14
C145,720y3.9x10-12[~=]0.11.16.6x1014neg
S34SO411S3887d.9.2x10-80.264.181.5x1016neg
S36SO411S375m.2.3x10-30.140.01365.0x10130.032
Cl35Cl4.9Cl36
S35
2x105y
87d.d
1.1x10-13
9.2x10-8
42e
0.34
75.4
75.4
1.2x1017
1.2x1017
neg
10-2
Cl37Cl4.9Cl3838.5m3.0x10-40.624.64.0x101614
F19F0.1F2012S.5.8x10-20.0091003.35x10153.5
N15NO30.1N1635S.2.0x10-20.0000130.3651.2x1013neg
O18Water
Itself
106O1929.4S.2.4x10-20.00020.2046.8x1019653

The O19 activity of 653/3.7x104 = 0.018 [mu]c/ml is thus dominant initially.

Since its half-life is half a minute, there will be no danger by the time the
discharged water reaches points of possible exposure.

The Cl38 activity corresponds to 3.8x10-4 [mu]c/ml which is of the order of maximum
permissible concentration for drinking water.

Since all other elements lie below these, the overall danger is believed to be
negligible.


Notes:

aProgram Administration and Installation Design of the Nuclear Reactor Project
at N. C. State College
, C. K. Beck, et al.

bSupplied by Mr. John Andrews, Raleigh Public Utilities Dept. Letter of July
27, 1950
to A. C. Menius. (ppm = number of atoms per molecule of H2O;
0.0335 x 10+24 H2O per cm³)

cNuclear Data, U. S. Dept. of Commerce, National Bureau of Standards, Sept. 1, 1950

dReaction Cl35(n,p)S35.

eAssuming [sigma]cl = 32 is principally due to its lighter isotope.