Fraction of ionized atoms in an intrinsic semiconductor

1. The problem statement, all variables and given/known data
Here is the problem in the book:

Here is the solution:

What I don’t get is why the solution defines the fraction to be ni/(5*1022). Shouldn’t it be 2*ni/(5*1022) since we have both donors and acceptors, so there are actually twice the number of atoms.

Also, intrinsic means that the silicon is not doped right? If that is the case why are there even donors and acceptors, shouldn’t the concentrations be zero?

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