De Broglie's Hypothesis | Definition | Explanation | De Broglie's Formula | thetutee

 

De Broglie hypothesis says that all matter has both particle and wave nature. The wave nature of a particle is quantified by de Broglie wavelength defined as λ=h/p where  “p”  is the momentum of the particle. This was called a hypothesis because there was no evidence for it when it was proposed, only analogies with existing theories. (The wavelength-momentum relation holds exactly for photons.)

 

The de-Broglie's hypothesis states that since a light, or any other electromagnetic wave, can also exhibit the properties of a particle, similarly, a particle should also exhibit the properties of a wave, and that those two natures are interchangeable if certain physical conditions exist to allow that change.

 

This hypothesis has been proved to be true so far, as many experiments on particles showing wave properties have shown that dual nature to exist, like electrons when passed through a double slit on a screen, get deposited on a screen opposite to the slits with different linear densities, and with alternate regions of high and low intensities of deposition, in accordance with the two-slit interference phenomena observed in the case of light waves, and which can only be possible if the electron exhibits some kind of wave nature when it strikes the two slits, undergoing constructive and destructive interference while remaining in that state, and then striking the screen as a particle again.

 

Historically, de Broglie hypothesis was the next step in quantum theory after Planck, Einstein, and Bohr.

 

• In 1900, Max Planck introduced the notion that radiation is quantized to derive the black body radiation spectrum.

• In 1905, Albert Einstein used Planck's idea to explain photoelectric effect, which led to wide acceptance of the quantum nature of radiation.

• In 1913, Niels Bohr used quantization of radiation along with the Bohr hypothesis (that the angular momentum of electrons is quantized) to correctly predict the line spectrum of hydrogen atom and explain.

• In 1923, Lois de Broglie took this idea further and proposed that matter has wave nature as radiation has particle nature.

Bohr hypothesis comes as an immediate consequence of de Broglie hypothesis - angular momentum must be conserved if an electron in an atom is seen as a wave going in circles around a nucleus such that the electron wave interferes constructively everywhere in the orbit.

 

In 1926 Erwin Schrödinger published the Schrödinger equation which generalized de Broglie's concept of matter waves and put them in a more robust theoretical footing.

 

The direct experimental confirmation came in 1927 when Clinton Davisson and Listor Germer and independently, GP Thomson observed electron diffraction.

According to planks wave equation energy is directly proportional to the frequency,

E α υ

E = hυ          where, h = 6.63×10-34 Js

So according to Einstein mass and energy are the manifestation of the same thing

E = mc²     

So, we can write by combing both equations,

hυ = mc²             (here c = 3.0 × 108 m/s)

as, υ = c/λ

h c/λ = mc²

λ = hc/ mc²

λ = h/mc      (Equation for light)

λ = h/mv      (Equation for matter) here v = velocity of the light, this equation is also known as de Broglie’s equation

λ = 1/mv      (where, mv = momentum)

From here we can deduce that the greater the mass of an object the lesser will be its wavelength.