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 83