If everyone is thinking alike, we cannot solve the hurdles of a problem. It seems true if we observe these hypotheses' hierarchy once. Italian physicist Francesco Maria Grimaldi discovered the wave phenomenon of light in 1665. But the uncertainty about light's nature was finally solved by Einstein's explanation of the photoelectric effect. Similarly, Neil Bohr succeeded in describing the structure of an atom with quantized electron orbits. But his stipulation of allowed stationary orbits was only a supposition until the discovery of the de-Broglie equation. Louis de-Broglie, a French physicist, presumed that moving microscopic and macroscopic objects are waves. He introduced a word called 'matter wave' to describe the waves of material objects in motion. As a result, matter exhibits a dual character of both particle and wave. Moreover, he derived an empirical formula to measure the wavelength of matter waves in 1923 called the de-Broglie equation.

1. De-
Broglie
equation
By,
Jayam chemistry
learners

2. Louis de-Broglie, a French physicist, presumed that moving microscopic and macroscopic objects are waves. He
introduced a word called 'matter wave' to describe the waves of material objects in motion. As a result, matter
exhibits a dual character of both particle and wave. Moreover, he derived an empirical formula to measure
the wavelength of matter waves in 1923 called the de-Broglie equation.
𝝀 =
𝒉
𝒎𝒗
Consider an object having mass m will move with a velocity of v and has a matter wave with a wavelength of
λ. Then by applying the de-Broglie equation, we have;
The de-Broglie equation to enumerate the wavelength of matter waves is useful for microscopic particles
such as electrons, protons, neutrons, atoms and molecules, positrons, etc., Due to their extreme low
wavelength values, it is not applicable for macroscopic objects. Still, it proved the dual character of matter
waves like light.

4. Davisson and Germer, in 1927, proved the wave phenomenon of electrons which served as practical evidence
for the de-Broglie equation. They used incandescent tungsten filament to produce a beam of electrons. And
this electron beam was accelerated in an electric field. Then the electron ray was allowed to fall on a nickel
crystal surface to split in different directions. It is known as grating. As a result, rounded dark and bright
diffraction rings of electron beams formed on a photographic plate. These concentric electron beam rings
resembled the X-ray diffraction pattern. It confirmed the wave motion of the electron.
If V is the potential difference applied in the electric field to accelerate an electron of charge e. Then the
wavelength of electron wave is;
𝜆 =
12.265 × 10−10 𝑚𝑒𝑡𝑟𝑒
𝑉

6. Significance of de-Broglie equation:
It described Neil Bohr’s quantized angular momentum condition mathematically.
According to Bohr’s atomic model, an atom can have an infinite number of stationary orbits. But the electron
rotates in permitted stationary orbits where the electron’s angular momentum is an integral multiple of h/2π.
Hence, all stationary orbits around the nucleus of an atom are not suitable for accommodating the electrons.
2π𝑟 = 𝑛λ
The above equation shows that an allowed stationary orbit with a circumference of 2πr holds an integral
number of de-Broglie wavelengths of an electron wave. Then the electron wave is said to be in phase.
When the stationary shell with 2πr circumference holds a fractional number of de-Broglie wavelengths of an
electron wave, then it is said to be out of phase. Due to the irregular pattern of crests and troughs in the
electron wave, the motion of the electron is not circular.