Question

Question #baa29

Answer 1

The wavelength of the light is 102.6 nm.

Explanation:

You use the Rydberg formula to calculate the wavelength, λ:

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

where

`R =` the Rydberg constant (`1.097 × 10^7color(white)(l) "m"^"-1"`)
`Z =` the atomic number of the atom
`n_1` and `n_2` are the initial and final energy levels

In this problem,

`Z = 1`
`n_1 = 3`
`n_2 = 1`

`1/λ = 1.097 × 10^7color(white)(l) "m"^"-1" × 1^2 (1/1^2 -1/3^2) = 1.097 × 10^7color(white)(l) "m"^"-1" (1/1-1/9)`

`= 1.097 × 10^7color(white)(l) "m"^"-1" × (9-1)/9 = 1.097 × 10^7color(white)(l) "m"^"-1" × 8/9 = 9.751 × 10^6 color(white)(l)"m"^"-1"`

#λ = 1/(9.751 × 10^6 color(white)(l)"m"^"-1") = 1.026 × 10^"-7" "m" = "102.6 nm"#