QUESTION FOUR [20 MARKS] QUESTION FOUR [20 MARKS]marks] a). A 2.5 MeV photon collides What is the momentum of emerges from the collision? [4marks] [5 marks] Compton effect.Using the law of conservation of energy and momentum show that lambda '=lambda +(h)/(M_(0)C)(1-cosTheta ) c). (i) A photoemissive surface has a threshold wavelength of 0.85mu m [5marks] threshold frequency and its work function in eV. [8 marks] calculate (ii) The maximum speed of the electrons emitted by violet light of wavelength 0.6mu m

a) To find the momentum of the photon emerging from the collision, we can use the Compton effect formula: where is the change in wavelength, is Planck's constant, is the rest mass of the electron, is the speed of light, and is the scattering angle.Given that the initial wavelength of the photon is , where is the initial energy of the photon, we can substitute this into the formula: b) To show that , we can use the law of conservation of energy and momentum.Let be the final wavelength of the photon after the collision. The initial momentum of the photon is , and the final momentum of the photon is .Using the law of conservation of momentum, we have: where is the momentum of the electron.Substituting the expressions for and , we get: Rearranging the equation, we have: Using the Compton effect formula, we can substitute : Simplifying the equation, we get: $p_{e} = \frac{h}{\lambda} - \frac{h}{\