Question #8ee4f

1 Answer
Jan 8, 2018

Answer:

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"#