Write de-Broglie hypothesis and derive equation of de-Broglie wavelength.

Explanation

If radiation has dual (wave-particle) nature why not particles of nature also exhibit wave like caharacter?
From this,scientist Louis Victor de-Broglie forwarded following hypothesis.
Moving particle of matter should display wave like properties under suitable condition.
Nature is symmetric and two basic physical entities-matter and energy then matter aslo posses dual nature.
De-Broglie showed that wavelength of particle is `lambda` and momentum is p then,
`lambda=(h)/(p)=(h)/(mv)`.......(1)
Where m=mass of partilce ,v speed of particle,h=planck.s constant.
From de-Broglie equation dual nature of matter can be easily observed.
Left hand side of equation represent wavelength `lambda` where as right hand side of equation has momentum (p) which is associated with particle.
Equation (1) is hypothesis for particle of matter .It is true for photon also,
`p=(hv)/(c)`
`therefore (c)/(v)=(h)/(p)`
`therefore lambda=(h)/(p)` where c=v`lambda` which can be associated with de=Broglie equation.
Thus,de-Broglie wavelength of photon can be associated with wavelength of electromagnetic wave.Thus,photon of radiation posses quantum energy and momentum.