How can the ionization energy of sodium be calculated knowing that the value of the wavelength at the Start of the continuum in the emittion spectrum is 242nm?

1 Answer
Jan 30, 2018

The ionization energy is #"494 kJ·mol"^"-1"#.

Explanation:

The value of the wavelength at the start of the continuum represents the ionization energy: the energy needed to remove a #"3s"# electron from a sodium atom (the red arrow in the diagram below).

Na levels
(Adapted from hyperphysics.phy-astr.gsu.edu)

The formula relating energy #E# and wavelength #λ# is

#color(blue)(bar(ul(|color(white)(a/a)E = (hc)/λcolor(white)(a/a)|)))" "#

If #λ = "242 nm"#, then

#E = (6.626 × 10^"-34" "J·"color(red)(cancel(color(black)("s"))) × 2.998 × 10^8color(red)(cancel(color(black)("m·s"^"-1"))))/(242 × 10^"-9" color(red)(cancel(color(black)("m")))) = 8.209 × 10^"-19"color(white)(l) "J"#

This is the ionization energy for one sodium atom.

For 1 mol of sodium atoms,

#IE = (8.209 × 10^"-19"color(white)(l) "J")/(1 color(red)(cancel(color(black)("atom")))) × (6.022 × 10^23 color(red)(cancel(color(black)("atoms"))))/("1 mol") = 4.94 × 10^5 color(white)(l)"J·mol"^"-1" = "494 kJ·mol"^"-1"#