The Rydberg equation should be used to solve this problem:
`1/lambda = R(1/n_i^2 -1/n_f^2)`
where lambda is the wavelength, R is the Rydberg constant, n-subf is the final n-level, and n-subi is the initial n-level.
We know that lambda = 91.63nm, R = 1.097 x 10e7, and n-subi = 1.
So, `1/(91.63x10^-9) = (1.097x10^7) (1 - 1/n_f^2)`
`(91.63x10^-9) x (1.097x10^7) = 1.005`
1/1.005 = .995
`.995 = 1 - 1/n_f^2`
1/n_fe2 = .005
1/.005 = n_fe2
sqrt (200) = n_f
The square root of 200 is closer to 14.14, so there's some rounding in the final answer, since n must be an integer. This error is mostly due to the inconsistent significant figures and abbreviated forms of the values for R and lambda.