Ionization Energy (Quantum Mechanics)

[vcollier]

Homework Statement

When ultraviolet radiation of wavelength 58.4 nm from a helium lamp is directed on to a sample of krypton, electrons are ejected with a speed of 1.59 Mm/s. Calculate the ionization energy of Krypton.

Homework Equations

E=hv, $\frac{1}{λ}$=R(1- $\frac{1}{n²}$ ) <- Lyman series
Ionization energy = $\frac{hcR}{n²}$

The Attempt at a Solution

I used the Lyman series to try and find the Rydberg constant for Krypton (with n=4), then substituted that value into the Ionization energy equation with n = 4 again. I'm given that the answer should be 14 eV, but I didn't get that result.

My confusion is how these equations relate to the ionization of krypton since the equations assume a single electron atom, which krypton is not. Furthermore, I can't find a use for the velocity (E= 0.5mv² also doesn't give the correct answer).

Any help in figuring out how to approach this problem would be greatly appreciated.

 

[voko]

Why do you care about the structure of krypton's spectrum? You have the energy of incident photons, you have the energy of emitted electrons. Where is the difference at?

 

[TSny]

The Lyman type of series only applies to one-electron atoms or ions. Try relating this problem to the photoelectric effect.