Appendix E
DERIVATION OF FORMULA FOR PERCENT MOLYBDENUM LEFT IN CLOUD
The formula given in Chapter 3 for the percent Mo”™ left in the cloud is based on a material balance for some nuclide, Y. It can be derived as follows:
Let
atoms Y formed in the explosion
YE
atoms Y left in cloud
atoms Y in fallout
atoms Mo™ formed in the explosion
atoms Moleft in the cloud
atoms Mo" in the fallout
fraction of Mo* atoms left in cloud
the ratio atoms Y: atoms Mo*® formed in thermal
neutron fission, a constant
[R* WY)g
R-value for nuclide Y in explosion
[R*(Yl¢
R-value for nuclide Y in cloud
[R* (Yeo
R-value for nuclide Y in fallout
Yg
Mop YE/Mop
Mog k [R®(Y)1p
since [R*(Y)]p = (Yp/Mopl/k
Yo
=
Moc Y¢o/Mog
Moc k (RY),
since [R®(y)) C
[YQ /Mocl/k
Yo = Moro Yro/Mogo
Moro k (R°) ro
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