Things that make no sense to me:
1. How did the population go from 400 to 4000 in about 100 years? That is rather intense rate of growth - population would have to double roughly every 30 years. I suppose it is theoretically possible in unrestrained conditions but there are a number of things that make it seem unlikely. 1st - female to male astronaut ratio is going to be at best 1:3 and probably 1:5. Maybe if every woman in the first generation had at least 5 kids and subsequent generations had 3-4 but still, given that there appears to be birth control and you would think a group of astronauts would have carefully calculated what population could be sustained for 200 years it seems a bit infeasible
2. So you have this mission that is critical to the survival of the human race - I know, let's give the job to teenagers! Wait, let's make sure to weed out any possible responsible teenagers first and give it to those who are most likely to disobey authority, give in to short-term thinking and instant gratification, and who generally don't have enough sense to come out of the (radioactive) rain.