Question

Electrons in a photoelectric-effect experiment emerge from a copper surface with a maximum kinetic energy of 1.10 eV . What is the wavelength of the light?

Answer 1

Answer: 213 nm

The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.

If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.

This is what Einstein proposed:  

Light behaves like a stream of particles called photons with an energy

$E=h.f$  (1)

So, the energy $E$ of the incident photon must be equal to the sum of the Work function $\Phi$ of the metal and the kinetic energy $K$ of the photoelectron:

$E=\Phi+K$  (2)

Where $\Phi$ is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal.

In the case of Copper $\Phi=4.7eV$

Now, applying equation (2) in this problem:

$E=4.7eV+1.10eV$  (3)

$E=5.8eV$  (4)

Now, substituting (1) in (4):

$h.f=5.8eV$  (5)

Where:

$h=4.136(10)^{-15}eV.s$ is the Planck constant  

$f$ is the frequency  

Now, the frequency has an inverse relation with the wavelength $\lambda$:  

$f=\frac{c}{\lambda}$ (6)  

Where $c=3(10)^{8}m/s$ is the speed of light in vacuum  

Substituting (6) in (5):

$\frac{hc}{\lambda}=5.8eV$   (7)

Then finding $\lambda$:  

$\lambda=\frac{hc}{5.8eV }$   (8)

$\lambda=\frac{(4.136(10)^{-15} eV.s)(3(10)^{8}m/s)}{5.8eV }$    

We finally obtain the wavelength:

$\lambda=213^{-9}m=213nm$