Answer :

we know the relation between energy and momentum P of a electromagnetic radiation having velocity C and energy E is


P = E/C


and we know energy of electromagnetic radiation is given by relation


E = h๐œˆ


Where E is the energy of Photon, ๐œˆ is the frequency of electromagnetic radiation and h is Planckโ€™s constant


So putting value of E in equation P = E/c


we get


P = h๐œˆ/c


We know relation between frequency wavelength and velocity of electromagnetic radiation as


c = ๐œˆ๐œ†


Where ๐œˆ is the frequency and ๐œ† is wavelength of electromagnetic radiation having velocity c


So re arranging we get


๐œˆ = c/๐œ†


Putting the value of ๐œˆ in equation P = h๐œˆ/c


We get


P = hc/ฮปc = h/๐œ†


Or we can say the wavelength of electromagnetic radiation is given as


๐œ† = h/P


Where h is Planckโ€™s constant and P is momentum of electromagnetic radiation


Now we know de Broglie wavelength of quantum (photon) can be given by relation


๐œ† = h/mv


Where ๐œ† is de Broglie wavelength of a photon having mass m and moving with velocity v (here the velocity of photon v = C)


But we know momentum is given by relation


P = mv.


So, substituting we get de Broglie wavelength of quantum (photon) as


๐œ† = h/P


This is same as wavelength of electromagnetic radiation


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