# Question 8ee4f

Jan 8, 2018

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"#