Question

Question #19476

Answer 1

The wavelength is 94.921 nm.

Explanation:

The Rydberg equation gives the wavelength for the transition:

`color(blue)(bar(ul(|color(white)(a/a) 1/λ = R(1/n_1^2 -1/n_2^2)color(white)(a/a)|)))" "`

where

`R =` the Rydberg constant (`1.0974 × 10^7color(white)(l) "m"^"-1"`) and
`n_1` and `n_2` are the numbers of the energy levels such that `n_1 < n_2`

`1/λ = (1.0974 × 10^7color(white)(l) "m"^"-1")(1/1 - 1/25) = (1.0974 × 10^7color(white)(l) "m"^"-1")× 24/25`

`= 1.0535 × 10^"-7"color(white)(l)"m"^"-1"`

`λ = 1/(1.0535 × 10^"-7"color(white)(l)"m"^"-1") = 9.4921 × 10^"-8"color(white)(l)"m" = "94.921 nm"`