dilution factor

[dinosaur93]

A solution of NaOH has a pH of 10. 10mL of this solution is mixed with 990mL of water. The pH of the diluted solution is closest to:

A. 8
B. 9
C. 11
D. 12


I know that the dilution factor is 10/990 so approximately 100x diltuon....so doesnt that mean that the pH has to be 12? but the answer states that it should be 8

[aishuwa1995]

[H₃O⁺]= 10^-10

NaOH ---> Na⁺ + OH^-

[OH^-] = 10^-14/10^-10 = 10^-4

C₁V₁=C₂V₂

10^-4 * 0.01 = C₂ * 1.00

C_{[OH^- new solution]}= 10^-6

[H₃O⁺] = 10^-14/10^-6

pH = -log[10^-8]
      =8