Chapter 1 HW Question 15 [ENDORSED]

[Lexy Swenson 1F]

For number 15 in Chapter 1 (atoms: the quantum world) of the Chemistry Textbook, I understand why n=1 (because it is the Lyman series), and I get the numbers they plugged in the Rydberg equation to find n=2, but I'm not sure how the solutions guide concludes that n2=3. Can anyone clarify this? Thanks! :)

[Marie_Bae_3M]

Oh that's because n2^2 is in the denominator and ~0.112=1/9. So basically 1/n2^2=1/9 basically means n2^2=9 and n2=sqrt(9)=3 :)