Question #19476

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Answer 1 · 2017-12-29T20:14:28

The wavelength is 94.921 nm.

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 $n_1 < n_2$

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

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

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