De Broglie

Louis de Broglie was born in 1892 and conducted initial experiments in his brother’s laboratory. Building up on Einstein’s theory, he proposed that any sort of matter has a dual nature and can be viewed as waves. Using the momentum of these matter waves, he also gave the famous formula for de Broglie wavelength. For his significant contribution in the field of physics he won the Nobel Prize in the year 1929. De Broglie’s concept is regarded as one of the most important formulas and theory wise statements in physics especially in classe 11. It is important in the form of preparation for competitive exams.

Who is Louis de Broglie?

Born on August 15, 1892 was a French physicist and nobel prize winner. His field in physics was under the study of quantum theory. His PhD thesis became the famous concept of De Broglie as what we know today.  He initially started out his work with X-rays in his brother’s laboratory. De Broglie won a Nobel prize in 1929 after his thesis was experimentally proved. He passed away on 19 March 1987.

What is the De Broglie Thesis?

As mentioned before, the thesis of Louis de Broglie’s PhD was what we know today as the De Broglie concept and De broglie Hypothesis of matter waves. 

The De Broglie hypothesis of matter waves states that all matter assumes wave-like nature and the wavelength can be related to the momentum of the matter.

De Broglie built up his hypothesis after Albert Einstein had proposed and found his photon theory to be valid.

What is a de Broglie wave?

In simple words, a de Broglie wave is called the matter wave. It is any wave that follows all the rules and inhibitions mathematically put down for how a wave should behave. 

De Broglie Concept of matter waves

He proposed two statements:

1. Matter and electromagnetic radiation make up the whole universe. Both being forms of energy can be changed into one another.
2. Matter loves symmetry. If this is the case, since radiation possesses dual nature then matter should too exhibit dual nature.

Building up on Einstein’s equation of momentum, p and wavelength de Broglie proposed a relationship that would hold true for any matter. It could be used to determine the wavelength of any matter. The relationship is as follows:

λ=h/p

Where p is momentum and h is Planck’s constant.

The wavelength that is derived when the equation is solved is called the de Broglie wavelength.

Derivation of de Broglie wavelength

The energy of a photon is given by;

E=h/λ where =c/λ

E= hc/λ …(1)

According to Einstein’s theory of relativity;

E= mc2 …(2)

From equation (1) and (2),

m= hc/λ

Therefore momentum of photon, 

p= mc= hc/cλ= h/λ

In other words:

λ= h/p

Significance of de Broglie hypothesis of matter waves

The de Broglie hypothesis of matter waves or de Broglie concept helped the field of quantum theory immensely. The concept of de Broglie wave showed that dual property was not only applicable to light but also matter waves and radiation. The de Broglie concept paved the way to the study of particle physics and atomic structure.

Experimental Proof

Despite having studied the wave nature of matter and proposing the de Broglie concept, there was still no experimental proof. Finally two physicists, Clinton Davisson and Lester Germer, in the year of 1927, found conclusive proof to de Broglie’s hypothesis. They conducted an experiment where electrons were fired at a crystalline nickel target. The results that they got went hand in hand with de Broglie’s wavelength.

The famous double slit experiment also proves his theory.

SI Unit of de Broglie wavelength

Generally, the de Broglie wavelength unit is in meters, but since it is very small, it is often expressed in nanometers or angstroms.

Conclusion

To sum up, the de Broglie concept states that just like light, matter and radiation also possess dual nature. Matter and radiation both being forms of energy are interchangeable. He used Einstein’s theory of relativity to derive the formula for de Broglie wavelength, which is λ=h/p. For this contribution, Louis de Broglie was awarded the Nobel Prize in the year 1929.