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 <u>under certain conditions. </u>
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 <u>energy</u> of the incident photon must be equal to the sum of the <u>Work function</u> of the metal and the <u>kinetic energy </u> 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.
<u>To understand it better:</u>
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.