Answer: -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
[tex]E=h.\nu[/tex] (1)
So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the kinetic energy [tex]K[/tex] of the photoelectron:
[tex]E=\Phi+K[/tex] (2)
Where [tex]\Phi[/tex] 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 [tex]\Phi=5 eV[/tex]
So, applying equation (1) in this problem:
[tex]E=h \nu[/tex]
Where:
[tex]h=4.136(10)^{-15}eV.s[/tex] is the Planck constant
[tex]\nu[/tex] is the frequency
Now, the frequency has an inverse relation with the wavelength [tex]\lambda=400(10)^{-9}m[/tex]:
[tex]\nu=\frac{c}{\lambda}[/tex] (3) Being [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum
[tex]\nu=\frac{3(10)^{8} m/s}{400(10)^{-9}m}[/tex] (4)
[tex]\nu=7.5(10)^{14} Hz[/tex] (5)
Substituting (5) in (1):
[tex]E=(4.136(10)^{-15}eV.s)(7.5(10)^{14} Hz)[/tex] (6)
[tex]E=3.102 eV[/tex] (7)
Now, substituting (7) in (2):
[tex]3.102 eV=5 eV+K[/tex] (8)
Finding [tex]K[/tex]:
[tex]K=-1.898 eV[/tex] (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 [tex]E[/tex] must be greater than the work function [tex]\Phi[/tex]
[tex]E>\Phi[/tex]
If [tex]E<\Phi[/tex] (as in this situation) photoelectric effect cannot occur.
