Question

Question #8ee4f

Answer 1

The wavelength is 102.5 nm.

Explanation:

The Rydberg equation gives the wavelength `λ` 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`

The second line in the Lyman series corresponds to a transition from (`n = 3`)
to (`n = 1`).

`1/λ = (1.0974 × 10^7color(white)(l) "m"^"-1")(1/1 - 1/9) = (1.0974 × 10^7color(white)(l) "m"^"-1")× 8/9`

`= 9.755 × 10^"6"color(white)(l)"m"^"-1"`

`λ = 1/(9.755 × 10^"6"color(white)(l)"m"^"-1") = 1.025 × 10^"-7"color(white)(l)"m" = "102.5 nm"`