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?

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

 (1)

So, the energy of the incident photon must be equal to the sum of the Work function of the metal and the kinetic energy of the photoelectron:

 (2)

Where 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

Now, applying equation (2) in this problem:

 (3)

 (4)

Now, substituting (1) in (4):

 (5)

Where:

is the Planck constant  

is the frequency  

Now, the frequency has an inverse relation with the wavelength :  

(6)  

Where is the speed of light in vacuum  

Substituting (6) in (5):

  (7)

Then finding :  

  (8)

We finally obtain the wavelength:

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