Einstein’s Explanation of Photoelectric Effect

Einstein explained the photoelectric effect using Planck’s formula. According to Planck’s formula, the light was a beam that had several particles. In this article, we will understand how Einstein explained the photoelectric effect and why earlier scientists failed to do this.

Why Did Scientists before Einstein Fail to Explain the Photoelectric Effect?

This concept came into the picture in the year 1887 by Heinrich Hertz. It was further researched and observed by Lenard in 1902. The photoelectric effect is a phenomenon wherein electrons get emitted from the metal when the light of substantial frequency is incident on it. 

Hertz believed that the wave theory would surely explain the photoelectric effect; however, it could not be due to the following reasons:

1. As per the wave theory, energy gets distributed uniformly across the wavefront and is mainly dependent on the beam’s intensity. This meant that the kinetic energy of electrons would increase with that of light intensity. 

2. As energy depends on the wave theory intensity, the light of low intensity should emit electrons after some time so that the electrons can acquire a sufficient amount of energy to emit. But emission of the electron was spontaneous irrespective of the intensity of light.

3. The wave theory says that light of any frequency must eject electrons. However, the emission of electrons only happened for frequencies greater than that of a threshold frequency (v0).

Explanation by Einstein of the Photoelectric Effect

Einstein’s theory of  photoelectric effect is based on the revolutionary idea of Planck that light was a particle. The energy transferred to every light particle, quanta or photon depends on the frequency (v) of light, shown by the photoelectric effect equation.

E= hv

Where h= Planck’s constant= 6.6161 x 10-34 Js.

Light is a collection of photons. Hence,  Einstein stated in his theory that when a photon comes in contact with a  particular metal’s surface, photon energy gets transferred to an electron. However, the electrons present on the top layer of the metal absorb all the kinetic energy transferred by a photon. Thus, the electrons near the outermost surface of metal have the highest kinetic energy.

Hence, 

The Photon energy = The Energy needed to remove the Electron (The Work Function) + Electron Kinetic Energy 

E= W + KE

hv= W + KE

KE= hv-V

Hence, we can say that at threshold frequency, v0, the electrons get ejected. Also, it is important to state that below v0, no electron will be removed from the surface. Hence, the work function of a metal is directly related to the threshold frequency (v0).

w= hv0

Also, the maximum kinetic energy equation is now

KE = 12mv2max= hv-hv0—-(1)

12mv2max=h(v-v0)

The stopping potential is Eνo= 12 mv2max ——(2)

Thus, by combining both the equations related to 1 and 2, we get:

Ev0=12mv2max=h(v-v0) 

Explanation of Certain Scientific Terms

In the above explanation, you must have come across certain scientific terms related to the photoelectric effect; let us take a look at them.

1. The Threshold Frequency

The threshold frequency is the least frequency of the incident light beam that is given, which is required for the electron emission from the metal surface.

2. The Work Function

 The energy that is required for the removal of the electron from metal’s surface is known as the work function.

3. The Stopping Potential

This is the potential that is required in order to stop the electron emission from the metal’s surface, which is also known as the stopping potential.

When we study Einstein’s explanation of the photoelectric effect, it is quite important to know about Planck’s theory as the photoelectric effect was based on it.

Planck’s Theory and the Photoelectric Effect

Planck’s theory stated that metals released electrons when they were exposed to high photons or light energy. Also,  kinetic energy released by electrons depends on radiation frequency v and not on its intensity. For instance, the frequency is 0 for an arbitrary metal, where there are no electrons released. Additionally, there is no delay between the removal of electrons and the interaction of light with the surface.

The two assumptions of Einstein explained these effects:

1. Light is a collection of photons, and Planck’s equation derives their power.

2. A single metal atom can absorb an entire photon. Hence, according to Einstein, light isn’t a wave, but they are made of energy particles called photons.

Functioning of the Photoelectric Effect

In 1905, Einstein introduced the theory of shock, which was based on Max Planck’s theory that light is composed of tiny packets of energy known as photons. Each packet contained Hv of power equal to the frequency v of the corresponding electromagnetic wave. The Planck constant is named after the constant of proportionality known as h.

Also, it is essential to note that Niel Bohr contributed significantly to the development of the photoelectric effect. He found out that the radiation from different gaseous atoms consisted of a different set of wavelengths.

As per the model proposed by Bohr, the electron quantum leaps between the orbits. These orbits prove Plank’s observations that atoms absorb or emit electromagnetic radiation in certain units, known as quanta. 

Conclusion

Hence initially, the photoelectric effect was discovered by Hertz and Lenard; it could not do justice to the equation given by Planck. The explanation given by Einstein helped clearly define the photoelectric effect. According to Einstein:

1. Light is a collection of photons. When a photon interacts with metal, photon energy gets transferred to an electron present on the metal surface.

2. However, the surface electrons carry all the kinetic energy imparted by the photon and have the maximum amount of kinetic energy.

3. The energy carried by light is defined as quanta or photon.

4. The value of 1 photon depends on the frequency of light.