Wave properties of particles

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Wave nature of light
The scientists Max Planck and Albert Einstein made great progress in the early 1900's in understanding the properties of light in terms of particles known as photons where the energy of the photons depended on the frequency (wavelength) of the light wave.  These studies are the basis for the branch of physics that is known as quantum physics. 

Calculating energy of light emitted by excited hydrogen atoms
Inspired by the work of Planck and Einstein, Neils Bohr developed an empirical equation that enabled calculation of the energies of light emitted when hydrogen gas is compressed and electrified.  Unfortunately Bohr's equation could not predict the frequency of light emitted from elements other than hydrogen.

Recognising the wave-particle duality of the electron and confirming it by experiment
λ =h
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Louis de Broglie sought to expand Bohr's work and, while doing so, hypothesised that all matter (not only photons) had a wave properties.  He developed an equation that allowed calculation of wavelength of any object from Planck's constant and the mass and velocity of the object.  This relationship was very important because it could be tested by experiment.  The experiments that confirmed de Broglie's hypothesis were carried out three years after the equation was proposed.
 
Planck's constant is very small (6.63 × 10–34 J s). For the wavelength of an object to be in the range where the wavelength can be measured(10–12 m to 10–2 m) the product of the mass and velocity of the object must be very small (10–32 to 10–22) as for small particles like electrons and neutrons.

Macroscopic (objects that we can see) have a large mass relative to Planck's constant. Therefore their wavelength is very small relaitve to the object and cannot be measured. Thus the wave-properties of large objects are not observable.

The importance of de Broglie's work that established the wave-particle duality of the electron is that it suggested that the properties of the electron could be described using equations used to describe waves. This was a major breakthrough because this enabled development of equations that went beyond that of Bohr and enabled calculation of electron energy for any atom.