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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