In this post, we will start our discussion with a series of new developments in the field of atomic chemistry, which changed the way we look at the matter. As scientists dug deeper, they were forced to abandon everything they believed in earlier and discover a whole new science- a science which seemed implausible even to the geniuses who were discovering it! Let us begin our journey into this new revolutionary science, which is fundamental to all modern branches of science today.

Before we start discussing the wave-particle duality concept let us first try to understand the difference between the two. What is a wave? What is a particle? And how are they different from each other in the classical sense?

According to classical physics, a **particle** of matter can be visualized as an entity having a finite *rest mass *i.e when the particle is at rest, it has some mass. It occupies some volume and has physical dimensions. For example, consider a football. It is made up of many particles and hence its matter. We can measure its mass/ volume. Moreover, unlike waves, particles are localized in space.

**Waves** are vibrations that have crests and troughs. They propagate in space with a definite frequency. Thus, waves have frequency, wavelengths, and amplitude.

There are two types of waves –

A] **Progressive waves** – They move continuously forward in a given direction. All photons in these waves vibrate. They propagate or travel continuously in space. This sine wave pattern continues to move in an uninterrupted fashion until it encounters another wave or until it encounters a boundary.

*e.g.*Sunlight

B] **Stationary waves** – These are vibrations confined to a particular region. Thus, they are called stationary or standing waves. These waves vibrate only in a restricted area. Suppose, we have a string that is bound at two points – it will only vibrate between these two points and will not travel any further. The waves thus created are stationary waves. e.g. Guitar string. When one plucks a string of a guitar, it vibrates thus creating stationary waves.

It was already revealed by Max Planck and Albert Einstein that light is made of photons(*meaning – visible light particle*). A photon is an elementary particle of light, which has no mass. It is just an energy packet with a discrete amount of energy. Thus, waves were modeled as particles to explain some phenomena.

According to the Planck-Einstein relation, 1)Energy of a photon,

**E = h𝓿**, where,

h = Planck’s constant and

𝓿= frequency of radiation.

2)Momentum **p = h/λ**

λ = wavelength.

**In 1924,Louis de Broglie asked a question that changed the perspective of how matter was conceived.**

Louis Victor de Broglie was born in one of the most illustrious families in France, in 1892.De Broglie was educated at home by private tutors. He started studying history but switched to studying law, pertaining to the lack of good teaching methods in history. At the age of 18, he graduated with an Arts degree. His elder brother was a theoretical physicist, and Louis de Broglie suddenly developed an interest in that subject. He did his Ph.D. in Physics. This French physicist developed a theory that helped classical science take a leap into modern science.

In 1924, he published his Ph.D. thesis, which was less than 100 pages long. In his thesis, he asked a very interesting question. He wrote –

“If a photon, which has no mass, can behave as a particle; does it follow that,an electron ,which has mass, can behave as a wave?”

His thesis provided an answer to this question. He proposed that, if an electron were to behave as a wave, its wavelength would be given by the following equation –

#### **λ**_{e} = h/p = h/mv

_{e}= h/p = h/mv

λ_{e} = wavelength of an electron.

h= Planck’s constant

p= momentum

m= Mass of the electron.

v=velocity of the electron circulating in an orbit.

* Note *– Though the mass of an electron is negligible as compared to a proton or neutron, it invariably does have some finite mass.

Note that, momentum(p=mv) is a characteristic property of moving particles. Wavelength is a characteristic property of waves. Thus, de Broglie’s equation gives us a relation to explaining* the wave-particle duality.*

This prediction by De Broglie was remarkable as it supported Bohr’s theory of quantization of stationary states within the atom! How? Let us see…

According to Bohr’s quantum condition, which we have already discussed in post 23,

the angular momentum L = mvr = nh/2π , where n= 1,2,3…

Now, if an electron is behaving as a wave, it has to be a stationary wave, as its orbit is fixed.

For the stationary wave to be in the orbit, there is a **GEOMETRIC constraint** on the wave – The circumference of the wave has to be an integral of the wavelength. (This is a rule in geometry. We just accept it as it is without getting into the details of this rule).

Thus,** Circumference of the orbit = n (wavelength of the wave)**

∴ **2πr = nλ**, r = radius of the orbit in which the electron is orbiting.

But according to De Broglie’s theory, λe = λ= h/mv. Substituting the value of λ in the above equation, we get,

**2πr=n×**(h/mv)

Rearranging the terms, we get,

**mvr = nh/2π !!!!!! **

**THIS IS THE BOHR”S QUANTUM CONDITION !!!!**

So, Bohr’s quantum condition just falls out of de Broglie’s predictions! Thus, this theory provided a compelling validation to the Bohr Model. This theory was an awe-inspiring revelation! Albert Einstein, who also was a theoretical physicist, loved De Broglie’s thesis!

So, basically what the thesis meant was that, just as we can model waves as particles, we could also model particles as waves! As we know, light (a wave ) is made up of photons(particles), an electron (which is a particle) can behave as a wave! This phenomenon was termed as ‘WAVE -PARTICLE DUALITY’, which means waves as well as particles/matter exhibit dual nature- they sometimes behave as matter and sometimes as waves! De Broglie’s waves of matter came to be known as** ‘MATTER WAVES‘.**

So, was this theoretical prediction about matter waves true? If yes, how was it proved by experimental data? We shall find the answers to all these questions in my next post. Till then,

Be a perpetual student of life and keep learning…

Good day!

References and Further Reading –

1)http://www.physicsclassroom.com/Class/waves/u10l4a.cfm

2)https://en.wikipedia.org/wiki/Matter_wave

3)http://broglie.poldow.com/1.htm

4)Lecture 6, MIT Solid-state Chemistry.

Image sources –

1)https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcS1hKDtOdpt_GBpKAfyZ5iE8cJSynOb2bwI61JJRvXvZFEFTQls5g

2)https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcSwHFjrGi_H0LRMXxHx9U7JiK9SwxijALZXfCZNcBDYlT1dm1Q

3)https://en.wikipedia.org/wiki/Louis_de_Broglie#/media/File:Broglie_Big.jpg

thank you this helped a lot

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Thank you 🙂

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this is mindblowing… amazing!

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Thank you 🙂

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