A Single solo player encounter’s a single NPC (1st level dragon born sorcerer) and defeats them in combat. How much XP do you award for this encounter and why. Please show your work thanks in advance.
For NPCs designed using the character creation system in PHB, I reward 50 XP for defeating a level 1 NPC, and double the previous XP reward for each level after (100 for level 2, 200 level 3, 400 level 4, etc). I might tweak this experience at higher levels, but my players are all level 3 right now and they haven't fought any NPCs higher than level 4.
edit: to clarify the why, I'm trying to keep it in line with the XP rewards presented for various creatures in the PHB appendix. I haven't even glanced at the pre-made adventures like Mines or Tyranny, so I have no idea what XP rewards NPCs give there. That would be a good place to look, though, if you seek further guidance before the MM and DMG come out.
Assume that it would have been a deadly encounter for one 1st-level PC. Deadly because if they were evenly matched it could have gone either way, 50/50 the PC got killed. The chart in the DM Basic download gives 100xp for that.