Question

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?

Answer 1

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).

(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"`