one more question 17-70 f3.5-4.5 lens vs 50mm f/1.8 SAM DT Lens

so my a100 camera came with a 17-70 f3.5-4.5 lens, i bought an a550 body only for higher FPS for my kids playing sports etc....

so around the house I use the 17-70 f3.5-4.5 lens and it works ok

50 mm F1.8 $140 lens

my question is if I buy the $140 50mm f1.8 sam dt lens i realize that i will not be able to zoom in and out it's just a static distance.  However because the F value is lower it will let in more light and the image will appear sharper or brighter is that correct?

Sorry please dumb down your answers, I know a little more than point and shoot people but not as much as a lot of people here, thanks as always you are all awesome!!