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 ![\Phi](https://tex.z-dn.net/?f=%5CPhi)
![E>\Phi](https://tex.z-dn.net/?f=E%3E%5CPhi)
If
(as in this situation) photoelectric effect cannot occur.