Assuing we survive, find a way to deal without fossil fuels, find a way to recycle all garbage and waste, here is what I think might happen:
Graphene will be the major player for all technologies. It's cheap and much, much better than anything at the moment. Graphene will be used in everything from cell phones to solar panels. In solar panels, graphene could make them up to 90% effecient (currently they are at most 25% effecient), this could solve a lot of energy issues in the future. Graphene also uses far, far less power than normal circuits. Cell phone batteries will last over a year before you need to recharge them because graphene can do the same thing as today's chips but use far, far less power.
Quantum computers will be in the experimental stages but not ready for purchase by consumers. They are much more complex and crazy then you can imagine so physicists will have a tough time making them do even the easiest calculations, but they will be in a rough working format.
Speaking of physics, the higgs bozon will probably be found by then, opening up a new chapter in the quantum physics saga. I hope gravity is almost completely understood by then so we can start generating our own gravitational fields.
That's all I can think of at the moment.
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