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Photon and its energy and momentum...

Photon and its energy and momentum

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If E and P are the energy and the momentum of a photon respectively,then on reducing the wavelength of photon

If E and P are the energy and the momentum of a photon respectively then on increasing the wavelenght of photon

Assertion: if wavelength of light is doubled, energy and momentum of photons are reduced to half. Reason: By increasing the wavelength, speed of photons will decrease.

Statement-1: Photon has definite momentum though it has no rest mass. Statement-2: Momentum of photon is due to its energy and therefore it has equivalent mass.

(a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K_1 and momentum p_1 . If the momentum of the proton is doubled, so p_2 = 2 p_1 , how is its new kinetic energy K_2 related to K-1 ? (b)A photon with energy E_1 has momentum p_1 . if another photon has momentum p_2 that is twice p_1 , how is the energy E_2 of the second photon related to E_1 ?