Fundamentals of matter structure

Photoelectric effect

The photoelectric effect is the phenomenon therefore a metal, if exposed to a light radiation, starts to beam electrons.

The classical physics arrive to explain some aspects, like:

• when the light hit a piece of matter, electrons are emitted because the electric field associated with the electromagnetic radiation (the light) provide energy at the electrons of the metal, then they can abandone the metal.
• the number of the electrons increase if increase the intensity of the light radiation

But these arguments are not explained by the classical physics:

• electrons are emitted with a kinetic energy that is in linear dependence with the frequency of the light radiation, and not in dipendence of the intensity of the radiation.
• It exists a threshold frequency ν₀ under that there isn't any emission of electrons. For the metals ν₀ is in the visible spectrum. Each matter has the own ν₀.

The experiment

A vacuum tube has two terminals, an anode and a cathode. There is a voltage generator between the two terminals, in series with an amperometer. There is a light radiation direct on the cathode.

If the potential on the anode is V_a ≤ 0 the electrons on the cathode are able to reach the anode, and the amperometer will signal a current flow.

Increasing the potential difference, will increase the number of electrons emitted that reach the cathode too, until we reach a saturation condition, therefore all the electrons emitted reach the cathode.

Now we suppose to trim the voltage generator and impress a negative voltage between anode and cathode.

We can see that starting with V_a = 0, and decrease the potential between anode and cathode, few electrons reach the anode, and with a specific value of V_a all the electrons are stopped.

This value of V_a is called stop potential V₀.

Einstein's explanation

Einstein try to explain the phenomenon with the theory of light quanta, also called photons. Einstein hypotesizes that light radiation is composed by particles called photons, and these are able to give their energy at the electrons of the metal, and these electrons so excited can abandon the material.

Each electron is tied with the material from an energy called Extraction work W₀, and each photon has an energy that:

E = hν
PHOTON ENERGY

h = 6.62606896(33)⋅10^-34 Js, Planck constant
ν = frequency of the incident wave.

The electron will leave the material only if hν > W₀. The maximum of the kinetic energy of the emitted electron will be:

K_m = hν - W₀
MAXIMUM KINETIC ENERGY

This because a part of the photon's energy will be spent to separate the electron from the material. This relation explain the linear dependence from the kinetic energy of the radiation frequency.

From the secon part of the experiment, we know that the the potential of V_a must furnish at the moving electron an energy in order to cancel its K_m. The potential is the energy, e = electron charge, the stop condition will happen when:

-V_a ⋅ e = K_m = hν - W₀

-V_a = K_m/e = (hν)/e - W₀/e

The stop potential will be the value of -V_a that verify that relation:

V₀ = (hν)/e - W₀/e
STOP POTENTIAL

This relation show the linear dependence of the potential from the radiation frequency.