Dual nature of radiation

Introduction

There are certain phenomena like interference, diffraction, polarization, reflection, refraction, etc which require a wave theory for their interpretation. Thus they hint at the wave nature of radiation. There are certain phenomena such as photoelectric effect, Compton effect, discrete emission, and absorption, etc. Which require a particle nature for their interpretation. Thus they hint that radiation consists of particles. According to Max. Planck ( 1900), the radiation consists of tiny bundles of energy such that energy of each bundle is E = h𝝂 where h is planck constant and  𝝂 is the frequency of radiation. This idea hints at the wave nature of radiation. According to Einstein, the energy of each bundle is E = mc² where m is the mass of the particle and c is the speed of light. Thus Einstein’s relation hints at the particle nature of radiation. All this indicates that radiation has dual nature i.e it exhibits itself as a wave in certain phenomena while it exhibits itself as a particle in other phenomena.

Laws of photoelectric emission

The experimental facts regarding photoelectric emission can be summarized in terms of the fundamental laws of photoelectric emission.

1. For the light of a given frequency, the photoelectric current is directly proportional to the intensity of light, provided frequency is above the threshold frequency.
2. For a given photosensitive material, there is a certain minimum frequency called the threshold frequency, below this photoelectric emission is not possible.
3. The process of photoelectric emission is instantaneous. As soon as the frequency of incident light exceeds the threshold frequency, the emission starts immediately without any apparent time lag( 10-9s).
4. The maximum kinetic energy of photoelectrons is found to rise with the rise in the frequency of the incident light, provided frequency exceeds the threshold limit. The maximum kinetic energy is however found to be independent of the intensity of light.

Explanation of Laws of Electronic emission

1. Einstein’s theory leads us to the conclusion that one photon of incident light would emit one electron from the metal. Therefore if the intensity of light is increased, the number of incident photons rises which results in raising the number of photoelectrons ejected. This is the first law of photoelectric emission
2. From Einstein’s photoelectric equation, it is evident that when the frequency of incident light is less than the threshold frequency, Kinetic energy is negative which means no emission of photoelectrons takes place for any intensity of light. This is the second law of photoelectric emission.
3. From Einstein’s photoelectric equation, it is evident that when the frequency of incident light is greater than the threshold frequency, the kinetic energy of photoelectrons ejected is directly proportional to the frequency and is independent of the intensity  This is called the third law of photoelectric emission.
4. In the photoelectric effect, there is an elastic collision between a proton and an electron. The electron absorbs the energy of the photon instantaneously and gets emitted instantaneously. This is called the fourth law of photoelectric emission.

Photoelectric Effect

In 1887, Hertz noticed that electrons are emitted from a metal surface when electromagnetic radiation falls on it. In 1888, Hallwachs showed experimentally that electrons are emitted from the Zinc plate when ultraviolet rays fall on the plate. This phenomenon of emission of electrons from a metallic surface, when illuminated by the light of appropriate wavelength or frequency, is called the photoelectric effect. The electrons radiated in this process are called photoelectrons and the current which is produced in the circuit is called photoelectric current. The photoelectric effect in general is a phenomenon exhibited by all the substances when illuminated by radiation of a suitable wavelength.

De Broglie Hypothesis:

This universe is composed of radiation and matter. Since radiation has a dual nature called the Dual nature of radiation, De Broglie concluded that matter must possess dual nature. The De Broglie relation is one of the frequently used equations to define the wave properties of the matter. It defines the wave nature of the electron. Electromagnetic radiation exhibits the dual nature of a particle and wave (which are expressed in frequency, wavelength). Microscopic particles as electrons also proved to possess this dual nature property. Louis De Broglie in his thesis advised that any moving particle, whether it is microscopic or macroscopic will be related to a wave character. It was called ‘Matter Waves’. He further suggested a relation between the velocity and momentum of a particle with the wavelength, if the particle had to behave as a wave. The particle and wave nature of matter, however, looked contrasting as it was not possible to prove the existence of both properties in any single experiment. This is because every experiment normally depends on some principle and results related to the principle are only reflected in that experiment and not the other. However, both the properties are necessary to understand or describe the matter entirely. Hence, particles and the wave nature of matter are interdependent. Both of these don’t need to be present at the same time though.

Significance of De Broglie relationship

The Importance of the De Broglie hypothesis is that it is more useful to microscopic and fundamental particles like electrons. De Broglie’s equation helps us to understand the idea of matter having a wavelength. Therefore, if we look at every moving particle whether it is microscopic or macroscopic it will have a wavelength. In cases of macroscopic objects, the wave nature of matter can be detected. De Broglie set out the following relation between wavelength (λ) and momentum (p) of a material particle. λ= hmv = hp Where, λ = wavelength, p = momentum, h= Planck’s constant m =mass, and v=velocity   Important Note

• De Broglie’s prediction was certified experimentally when it was found that an electron beam goes through diffraction, a phenomenon characteristic of waves
• Every object in motion has a wave character
• The wavelengths corresponding to the ordinary objects are so short (because of their large masses) that their wave properties cannot be detected

Derivation of de Broglie relationship

For a photon of light of frequency, We have the equation from Einstein’s momentum energy relation E = pc Where, E = energy p = momentum c = speed of light Light behaves as a wave when it undergoes interference, diffraction, etc., and is completely described by Maxwell’s equations. But then, the wave nature of electromagnetic radiation is labeled into question when it is embroiled in blackbody radiation, photoelectric effect, and such. Einstein forwarded his idea of the photon, a bundle of quantized radiant energy localized in a small volume, as a way to describe the particle-like nature of light. Now from Planck’s equation of wave nature of light, we can write as E = hν= hcλ Where h= Planck constant E=energy λ = wavelength c=speed of light Now as per de-Broglie, both these energies should be equal hcλ = pc λ = hp De, Broglie advised the above equation is a general one that applies to material particles as well as to photons. Now the momentum of the particle of mass m and velocity v is p=mv so its de-Broglie wavelength λ = hmv

Drawback

It is applicable on microscopic particles like electrons, protons, and neutrons but it fails in the case of large-size objects because they have more mass and their wavelength becomes smaller and that is not an easy task to measure.

Conclusion

De Broglie concluded that most of the particles are too heavy to observe their wave properties. if the mass of an object is very small, however, the wave properties can be explained experimentally. De Broglie anticipated that the mass of an electron was small enough to express the properties of both particle and wave. All matter expresses wave-like behavior. For example, a beam of electrons can be emitted the same as that of a beam of light or a water wave. In most cases, however, the wavelength is too small to have a practical effect on day-to-day activities. Hence in our day-to-day lives with objects the size of tennis balls and people, matter waves are not relevant. The de Broglie equations also describe the relationship between the wavelength λ and the momentum p, frequency f, and the total energy E of a free particle.