Minimum wavelength of electrons ejected from metal

1. Feb 13, 2016

auleiia

1. The problem statement, all variables and given/known data

This problem has two parts.

A laser produces photons having an energy, E = 3.5eV.
a) What is the wavelength of photons produced, assuming that the index of refraction is 1.6? ->221nm
b) If this laser beam is focused on the clean surface of a metal having a work function of φ=1.5eV in vacuum, what is the minimum wavelength λmin of the electrons that will be ejected from the metal? Assume that the experiment is done in a vacuum. -> .867nm

2. Relevant equations

E = hv/λ
KEmax = hf - φ

3. The attempt at a solution
So I understand part a. It's simply λ = hv/E, where v is calculated using index of refraction. However I am stuck on part B, where the answer is .867 nm. At first I was trying to do λ = hc/φ, since v = c since it is in a vacuum, and since the minimum frequency will be when KE = 0 then hf = φ, however that gives me 826nm which is not correct, or even close to being correct.

2. Feb 14, 2016

TSny

The question is asking for the minimum wavelength of the ejected electrons (de Broglie wavelength).