# De Broglie's relationship

As described above, radiations have to be considered as wavelike in order to explain certain experiments and also as particle to explain certain other experiments. This dual behaviour is commonly referred to as wave-particle duality.

In 1924, Louis de Broglie proposed that if light can display this wave-particle duality, then matter, which certainly appears to be particle like, might also have wavelike properties under certain conditions. Louis de Broglie was able to put this idea quantitatively by deriving a relationship between wavelength
Î» (characteristic of wave) and momentum p (characteristic of particle).This relation may be derived as follows:

Planck's relation
E = h
Î³ = hc/Î»

Einstein's relation
E = mc2 Equating these two expressions, we get mc =
Now, the term mc in the above expression may be considered to be the momentum p of the photon. Thus, we have
p =
For ordinary material particles, de Broglie suggested that c may be considered to be equivalent to v (i.e. their velocities) and thus it is also applicable to the material particles.

According to the above equation, particle and wave natures are inversely related to each other. If the mass of the particle is small, as in the case of subatomic particles, the wavelength is significant, i.e. for such particles, wave nature is expected. For a particle of larger mass, the wavelength is too small to be of any practical significance.