This transition corresponds to the second (aqua) line in the hydrogen spectrum.
The wavelength is given by the Rydberg formula
#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" × (1/2^2 -1/4^2) = 1.0974 × 10^7color(white)(l) "m"^"-1" (1/4-1/16)#
#= 1.0974 × 10^7color(white)(l) "m"^"-1"× (16-4)/(16×4) = 1.0974 × 10^7color(white)(l) "m"^"-1" × 12/64 = 2.0576 × 10^6color(white)(l) "m"^"-1"#
#λ = 1/(2.0576 × 10^6color(white)(l) "m"^"-1") = 4.860 × 10^"-7"color(white)(l) "m" = "486.0 nm"#
