One of the elements that makes Under the Dome a little different from most other science fiction on television is the way it can tell powerful stories without too many pyrotechnics, though Under the Dome is good at that, too. But in episode 1.7, we get the story of an emotionally traumatic birth - by Julia's neighbor, whose husband is locked outside the dome - and an even more traumatic death, of the woman who helps deliver the baby.
That would be Alice - Norrie's biological mother - who we already know is suffering from diabetes. But the energy she expends in guiding the birth is too much for her. And so the birth is sadly balanced by a heart attack for Alice, and her apparent death.
I say "apparent," because, in science fiction, nothing including death is ever completely certain. Even in straightforward police or detective or spy stories, death isn't certain, unless you see the victim blown to bits on the screen. (In 24, for example, Tony Almeida comes back, after being pronounced dead and Jack grieving to the max about that.) But in science fiction, even being shot in the head could lead not to death - if, say, the mind in the head is teleported to another body in time.
Nothing like that is happening (yet) in Under the Dome, but it's also clear that the regular rules just don't apply in this strange little universe of Chester's Mill. So when Norrie pleads with the nucleus, you just can't say for sure what's going to happen.
Probably nothing more, alas, in the case of Alice. But there's lots more in store for everyone else still Under the Dome, in this strange and original television series.