▁bottom ▁of ▁the ▁nuclear ▁valley ▁of ▁stability . ▁ ▁Introduction ▁The ▁line ▁of ▁beta ▁stability ▁can ▁be ▁defined ▁mathemat ically ▁by ▁finding ▁the ▁nuc lide ▁with ▁the ▁greatest ▁binding ▁energy ▁for ▁a ▁given ▁mass ▁number , ▁by ▁a ▁model ▁such ▁as ▁the ▁classical ▁semi - emp ir ical ▁mass ▁formula ▁developed ▁by ▁C . ▁F . ▁We iz s ä cker . ▁ ▁These ▁nu cl ides ▁are ▁local ▁maxim a ▁in ▁terms ▁of ▁binding ▁energy ▁for ▁a ▁given ▁mass ▁number . ▁ ▁All ▁odd ▁mass ▁numbers ▁have ▁only ▁one ▁beta ▁decay ▁stable ▁nuc lide . ▁ ▁Among ▁even ▁mass ▁number , ▁seven ▁( 9 6 , ▁ 1 2 4 , ▁ 1 3 0 , ▁ 1 3 6 , ▁ 1 4 8 , ▁ 1 5 0 , ▁ 1 5 4 ) ▁have ▁three ▁beta - stable ▁nu cl ides . ▁ ▁None ▁have ▁more ▁than ▁three , ▁all ▁others ▁have ▁either ▁one ▁or ▁two . ▁ ▁From ▁ 2 ▁to ▁ 3 4 , ▁all ▁have ▁only ▁one . ▁From ▁ 3 6 ▁to ▁ 7 2 , ▁only ▁nine ▁( 3 6 , ▁ 4 0 , ▁ 4 6 , ▁ 4 8 , ▁ 5 0 , ▁ 5 4 , ▁ 5 8 , ▁ 6 4 , ▁ 7 0 ) ▁have ▁two , ▁and ▁the ▁remaining ▁ 1 1 ▁have ▁one . ▁From ▁ 7 4 ▁to ▁ 1 2 2 , ▁only ▁three ▁( 8 8 , ▁ 9 0