# Threshold frequency and wavelength of electrons in the photoelectric effect

1. Dec 3, 2012

### Ezequiel

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

Electrons are emitted from a metal as a consequence of their absorption of energy from a light beam. Find the threshold frequency of the metal and the wavelength of emitted electrons.

Wavelength of incident light λ = 500 nm
Work function of the metal $\phi$ = 2.1 eV

2. Relevant equations

Threshold frequency:

f0 = $\frac{\phi}{h}$

3. The attempt at a solution

Threshold frequency:

f0 = $\frac{2.1 eV}{4.136 \times 10^{-15} eV·s }$ = 5.08 × 1014 Hz

Is this correct?

How can I find the wavelength of emitted electrons?

2. Dec 3, 2012

3. Dec 3, 2012

### Ezequiel

Thanks for the confirmation.

As I understand the photoelectric effect, one photon transfers all of its energy to an electron, so the energy absorbed by any electron must be the same (for a monochromatic beam), in this case hc/(500 nm) = 2.48 eV. Electrons need at least 2.1 eV to escape this metal, so they must have a maximum kinetic energy of 0.38 eV. Since not all of them have the same kinetic energy (due to losses) I assume they must have different wavelengths as well, how can I find the wavelength of emitted electrons?

4. Dec 3, 2012

### Staff: Mentor

You can assume that they all have 0.38 eV. If you like, use "<=" in the calculations, but that won't change much.

5. Dec 3, 2012

### Ezequiel

Ok, so it would be λ = $\frac{hc}{\sqrt{2mc^2K}} \approx$ 2 nm, right?