**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.**