Solve the equations to obtain the outgoing photon frequency 𝑓′ in the following form:𝑓′ = (−𝐵 ± √𝐵2 − 4𝐴𝐶)2𝐴where you are to determine the unknowns 𝐴, 𝐵 and 𝐶 in terms of 𝑓, 𝑐, 𝑛, 𝜃, and electron restmass 𝑚. You may use the fact that for general (relativistic) electrons, the dispersion relation is𝐸 = √𝑝2𝑐2 + 𝑚2𝑐4

n a medium of refractive index 𝑛, the wavelength of light 𝜆0 is related to its frequency 𝑓0 via the relation𝜆0 = 𝑐/(𝑛𝑓0) , where 𝑐 is the speed of light in vacuum. Fig. 1 is labelled with variables of relevance,including input photon frequency 𝑓, outgoing photon angle 𝜃, outgoing photon frequency 𝑓′, outgoingelectron angle 𝜙, outgoing electron energy 𝐸 and outgoing electron momentum 𝒑. In this problem, themomenta of all particles, before and after, lie entirely in the plane of the paper.1. Write the energy conservation equation and the momentum conservation equations for Comptonscattering for incident and outgoing photons in a medium of refractive index 𝑛. Explain youranswer in detail

Calculate the photon energy corresponding to this wavelength. Select the option that best matches your calculated answer.

What is the frequency of a photon with an energy of 3.38 𝑥x 10-19 J?A.1.96 𝑥x 1014 HzB.5.10 𝑥x 1014 HzC.4.47 𝑥x 1014 HzD.6.71 𝑥x 1014 Hz

Calculate the de- Broglie wavelength for an electron moving at 1.0 x 107 m/s.

Monochromatic light of frequency of 6×10^14 Hz is produced by a laser. Power emitted is 4×10−3W. Approximately how many photons per second are emitted by the source?