Somewhere between 40,000 and 130,000 rpm, but 60,000 to 90,000 would be considered best for efficiency and longevity!
You size the turbo [mix and match compressor wheels with turbine wheels in different size housings] so the the amount of exhaust gases and the heat differential will supply enough horsepower to turn the impeller wheel to supply the amount of boost you want at maximum ENGINE rpm while keeping its [turbo] rpm in the most efficient range as researched from the graphs supplied with each unit. Actually you may want to allow the efficiency to drop a little but peak at the HP peak rpm then slowly decline as you approach redline.
http://www.engr.colostate.edu/....html
Study the individual files you'll be an quasi-expert afterwardshttp://
www.gnttype.org/techarea/turbo/
The most efficient rpm gives the most boost with the least waste of power in over heating the output air.Each pound of boost can heat the air 10-20F depending on the efficiency of the unit at that rpm...adding an extra 10F means a 1% EXTRA HP loss from the total engine power.
Apples to apples without an intercooler 4.0-5.0% power gain per psi is good against the theoretical 6.6%!