Energy to remove a single electron
#"Energy for 1 electron" = (208.4 color(red)(cancel(color(black)("kJ"))))/(1 color(red)(cancel(color(black)("mol electrons")))) × ("1000 J")/(1 color(red)(cancel(color(black)("kJ")))) × (1 color(red)(cancel(color(black)("mol electrons"))))/(6.022 × 10^23 "electrons") = 3.461 × 10^"-19"color(white)(l) "J/electron"#
Wavelength of light
The formula for the energy (#E#) of a quantum of light is
#color(blue)(bar(ul(|color(white)(a/a) E = (hc)/λ color(white)(a/a)|)))" "#
where
#h =# Planck's constant
#c =#the speed of light
#λ =# the wavelength of the light
We can rearrange the formula to get
#λ = (hc)/E#
∴ #λ = (6.626 × 10^"-34" color(red)(cancel(color(black)("J·s"))) × 2.998 ×10^8 color(white)(l)"m"·color(red)(cancel(color(black)("s"^"-1"))))/(3.461 × 10^"-19" color(red)(cancel(color(black)("J")))) = 5.740 × 10^"-7"color(white)(l) "m" = "574.0 nm"#
