Q. 183.7( 15 Votes )

# Show that the wav

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

Where E is the energy of Photon, ๐ is the frequency of electromagnetic radiation and h is Planckโs constant

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

we get

P = h๐/c

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

c = ๐๐

Where ๐ is the frequency and ๐ is wavelength of electromagnetic radiation having velocity c

So re arranging we get

๐ = c/๐

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

We get

P = hc/ฮปc = h/๐

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

๐ = h/P

Where h is Planckโs constant and P is momentum of electromagnetic radiation

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

๐ = h/mv

Where ๐ 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 = h/P

This is same as wavelength of electromagnetic radiation

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