Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n at the...

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.