# 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.

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?

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