What is the maximum kinetic energy (in ev) of a photoelectron when a surface, whose work function is 5.0 ev, is illuminated by photons whose wavelength is 400 nm?

-1.898 ev (this means the photoelectric effect cannot occur)

Explanation:

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 surface.  

In this case  

So, applying equation (1) in this problem:  

Where:  

is the Planck constant  

is the frequency  

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

(3) Being is the speed of light in vacuum

(4)

(5)

Substituting (5) in (1):

(6)

(7)

Now, substituting (7) in (2):  

(8)  

Finding :

(9)  Since a negative kinetic energy is not physically possible, the only explanation is: the conditions for a photoelectric effect were not met, hence the photoelectric effect cannot occur.

To understand it better:

The main condition for the occurrence of the photoelectric effect is that the energy incident photon must be greater than the work function

If (as in this situation) photoelectric effect cannot occur.