de-Broglie equation
                     De-
Broglie 
equation
By,
Jayam chemistry 
learners
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 
mCoantsteidre wr aavne os binje 1ct9 h2a3v cinaglle md athsse  mde w-Bilrlo mgloiev ee qwuiathti oan v.elocity of v and has a matter wave 
with a wavelength of λ. Then by applying the de-Broglie equation, we have;
  𝒉𝝀=
𝒎𝒗
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.

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;
  12.265×10−10𝑚𝑒𝑡𝑟𝑒
𝜆=
√𝑉

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 
nuc  le2us of aπn atom𝑟 are no=t suitab𝑛le for accλommodating the electrons.
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.