FROM:

CC: Reactor Committee

In preparation for an earlier report^{a},

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 purity | Pars per^{b}Million of Water | Active tope | ^{c}life | [lambda](sec-1) | [sigma]a of^{c}Target (barns) | Abundance^{c}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 | 42^{e}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.

Notes:

^{a}Program Administration and Installation Design of the Nuclear Reactor Project

at

^{b}Supplied by

27, 1950

0.0335 x 10+24 H2O per cm³)

^{c}Nuclear Data,

^{d}Reaction Cl35(n,p)S35.

^{e}Assuming [sigma]cl = 32 is principally due to its lighter isotope.