January 16, 1952

In preparation for an earlier report^a, 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.

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)
Si30	SiO2	9.8	S31	2.7h.	7.1x10-5	0.12	3.1	1.0x1016	.017 .17?
Fe54	Fe	0.02	Fe55	3y	7.3x10-9	2	5.9	3.95x1013	neg
Fe58	Fe	0.02	Fe59	47d.	1.7x10-7	0.36	0.34	2.3x1012	neg
Ca44	Ca	8.7	Ca45	152d.	5.3x10-8	0.6	2.1	6.1x1015	neg
Mg26	Mg	1.4	Mg27	9.58m	1.2x10-3	0.05	11.3	5.3x1015	0.64
Na23	Na+K	4.2	Na24	14.9h	1.3x10-5	0.6	100	1.4x1017	2.2
C13	CO3 HCO3	3.9 14	C14	5,720y	3.9x10-12	[~=]0.1	1.1	6.6x1014	neg
S34	SO4	11	S38	87d.	9.2x10-8	0.26	4.18	1.5x1016	neg
S36	SO4	11	S37	5m.	2.3x10-3	0.14	0.0136	5.0x1013	0.032
Cl35	Cl	4.9	Cl36 S35	2x105y 87d.d	1.1x10-13 9.2x10-8	42e 0.34	75.4 75.4	1.2x1017 1.2x1017	neg 10-2
Cl37	Cl	4.9	Cl38	38.5m	3.0x10-4	0.6	24.6	4.0x1016	14
F19	F	0.1	F20	12S.	5.8x10-2	0.009	100	3.35x1015	3.5
N15	NO3	0.1	N16	35S.	2.0x10-2	0.000013	0.365	1.2x1013	neg
O18	Water Itself	106	O19	29.4S.	2.4x10-2	0.0002	0.204	6.8x1019	653

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.

^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.