You should reconsider whether you really want to breed widows! The spiderlings are minute, and could VERY easily escape, either through the air holes ( I assume you gave them some ) or when you open the lid to feed. If they escape ( which is likely), you could end up with an INFESTATION of widows - not a pleasant thing, even to an arachnid hobbyist. If you are sure you want to breed these, ( and are experienced enough to know what you're doing with this species ) then you should wait at least a week, to let the female get acclimated to her environment. Then introduce the male. If you don't want to lose your male, you may want to view the mating with an open lid, and have some kind of prod available. That way, if the female is not impressed, and mating does not take place , you can save your male and try again later. But first you should be sure that what you have IS a male. Male black widows look nothing like females. Here is the link to a picture of a MALE black widow :
http://home1.gte.net/cpq1cvvg/bwidowmale.htm
As far as what species you have, it is probably Lactrodectus hesperus, the western widow.