 # Einstein's Explanation of Photoelectric Effect

Albert Einstein, a German physicist, is considered one of the greatest scientists ever. He has contributed his work in the field of general relativity, black holes, photoelectric effect, and many more. In 1921, Einstein was awarded the Nobel Prize in physics for the discovery of the photoelectric effect.

### Introduction to Einstein Explanation of Photoelectric Effect

The discovery of the photoelectric effect was one of the greatest achievements of Einstein's life, and for which he received the Nobel Prize. Einstein was the first to suggest that light is both a wave and a particle. This is called the wave-particle duality of light. The wave-particle duality is the fundamental concept behind quantum mechanics and the reason behind the development of solar cells and electron microscopes.

According to the Photoelectric effect, when a metal surface is irradiated with light of sufficient energy, it causes the electrons of the metal to eject out.

So let us try to understand what the explanation behind the Photoelectric effect is.

The electrons present inside the atoms of the metal surface gain energy and start vibrating with high frequency, due to the oscillating electric field of the incident light. When the energy of incident radiation is higher than the work function of the metal, the electrons receive sufficient energy to eject out of the surface. The speed and number of emitted electrons depend upon the color and intensity of the incident radiation, and the time duration of incident radiation.

● When the intensity of incident radiation is more, the electrons receive more energy and vibrate more, so more electrons are emitted out with greater average speed.

● Incident radiation of higher frequency makes the electrons vibrate faster, thereby increasing the electron emission. Dim light normally doesn't provide the necessary energy for electron emission.

### What Is the Photoelectric Effect?

When incident radiation on light having energy greater than the threshold value of metal hits the surface, the tightly bound electrons of the metal are set loose. A particle of light is called a photo. When a photon collides with electrons, it imparts the sum of its energy to it, gaining which the electron ejects out of the surface. The remaining energy of the photon forms a free negative charge called photoelectron.

### Einstein Explanation of Photoelectric Effect

● The strength of the photoelectric current depends upon the intensity of incident radiation, and it should be higher than the threshold frequency.

● The reverse potential stopping potential was the photo-current stop. It is independent of the intensity of incident radiation.

● Photoelectric current does not occur if the frequency of incident radiation is below the threshold frequency. A metallic strip, when exposed to light or sun, will not be able to produce Photoelectric effect unless the frequency is greater than the threshold value.

● The photoelectric effect is an instantaneous process, as soon as light hits the surface metals come out.

### Einstein Theory of Photoelectric Effect

Einstein's idea about light was revolutionary and magnificent. He gave an efficient method of irradiation. Light has some tiny group of particles known as photons. These particles consist of higher energy, which is also called the quantum of radiation. Therefore, light is made up of packets of energy or quantum of energy. Photons carry momentum and energy from the source of light by which they are emitted.

### Einstein and His Equation of the Photoelectric Effect

According to Einstein-Planck relation,

E = hν …(1)

Where 'h' is the Planck's constant, and 'ν' is the frequency of the emitted radiation.

From the experiments of the Photoelectric effect, it is found that no electron emission occurs if the incident radiation has a frequency less than the threshold frequency. From the equation, you can know that energy is directly related to frequency, and this also explains the instantaneous nature of electron emissions.

When the photoelectron comes out of the metallic surface, it will be converted to purely kinetic energy as there is no electric field outside the surface. The quantum energy imparted by the photons is partly used by the electron to overcome the molecular attraction of the surface.

So, the kinetic energy of a photoelectron is = (energy imparted by photon) - (energy used to come out of the surface).

This energy is constant for a surface, and it is denoted by Φ. This is called the work function of a surface and is constant for a given material. Thus the equation is given as,

K.E. = hν – Φ …(2)

This is Einstein's photoelectric equation.

The same case happens with the photoelectrons. The electrons need minimum threshold energy to get ejected out of the surface. When electrons are imparted with a threshold frequency (v0), they acquire enough energy to eject out of the surface. If the electron gets energy equal to threshold frequency, its kinetic energy becomes zero after coming out of the surface. Using this we have

hv0 – Φ = 0 or hv0 = Φ ….(3)

Using in equation (2), we get K.E. = hν – hν0

or K.E. = h(ν – v0)

Also, v0 is the Stopping Potential, So

K.E. (max) = eV0; and putting this in equation (3), we have:

eV0 = h (ν – v0) ……(4)

Using this equation; the value of 'h' is calculated for the Photoelectric effect. The values obtained by this equation are in congruence with actual values, thus proving Einstein's explanation for the Photoelectric effect.