Question #baa29

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1 Answer
Ernest Z.
Mar 4, 2017

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"#

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