▁is ▁the ▁effective ▁f ission ▁cross ▁section ▁area . ▁Pe ier ls ▁did ▁not ▁perform ▁the ▁calculation , ▁leaving ▁this ▁task ▁to ▁Fr isch . ▁The ▁chem istry ▁of ▁u ran ium ▁was ▁not ▁well ▁known ▁at ▁the ▁time , ▁and ▁Fr isch ▁believed ▁that ▁its ▁density ▁was ▁; ▁the ▁true ▁value ▁is ▁more ▁like ▁. ▁The ▁f ission ▁cross ▁section ▁value ▁was ▁more ▁problem atic . ▁For ▁this , ▁Fr isch ▁turned ▁to ▁a ▁ 1 9 3 9 ▁Nature ▁article ▁by ▁L . ▁A . ▁Gold stein , ▁A . ▁Rog oz in ski ▁and ▁R . ▁J . ▁Wal en ▁at ▁the ▁Rad ium ▁Institute ▁in ▁Paris , ▁who ▁gave ▁a ▁value ▁of ▁. ▁This ▁was ▁too ▁large ▁by ▁an ▁order ▁of ▁magnitude ; ▁a ▁modern ▁value ▁is ▁about ▁. ▁Using ▁the ▁values ▁he ▁had , ▁Fr isch ▁calculated ▁the ▁value ▁of ▁the ▁mean ▁free ▁path ▁for ▁u ran ium - 2 3 5 ▁using ▁Av og ad ro ' s ▁constant : ▁ ▁Pe ier ls ▁and ▁Fr isch ▁claimed ▁that ▁the ▁critical ▁radius ▁was ▁about ▁ 0 . 8 ▁times ▁the ▁mean ▁free ▁path . ▁From ▁this , ▁Fr isch ▁could ▁calculate ▁the ▁volume ▁of ▁the ▁sphere ▁from ▁the ▁well - known ▁equation : ▁ ▁The ▁mass ▁then ▁comes ▁out ▁to ▁be : ▁ ▁Fr isch ▁and ▁Pe ier ls ▁then ▁considered ▁the ▁speed ▁of ▁a ▁u ran ium ▁f ission ▁chain ▁reaction , ▁exponential ▁in ▁nature , ▁where ▁" τ ▁is ▁the ▁time ▁required ▁for ▁the ▁neut