For full credit, show the starting equation in symbols. If it makes sense, solve in symbols before pluggingin numerical values. Remember, physical quantities with units have to have the units written down.Unless otherwise stated, keep enough sig-figs to produce a final answer accurate to three sig-figs1. X-rays with a wavelength of 4 =8.55 pm are used in a Compton scattering experiment(i.e. the photons are scattered by essentially free electrons).a. What is the energy, E, , of the incident photons in eV?b. When the Compton scattered X-ray scatters to an angle (measured from thedirection of the incident X-ray) of 0 = 115.0°, what is the wavelength of theCompton scattered X-ray?c. When the Compton scattered X-ray scatters to an angle (measured from thedirection of the incident X-ray) of 0 =115.0°, what is the change in energy for theX-ray photon in eV?d. When the Compton scattered X-ray scatters to an angle (measured from thedirection of the incident X-ray) of 0 =115.0°, what is the change in kinetic energyfor the scattered electron in eV? Quantum Mechanics (Matter Waves):Formula PagehcPhoton energy: E =hf =Photoelectric effect: Kmaxm,v2= hf -W, W is the work function, K=eVmax=stopmaxhEp =Photon momentum:h- = 2.4263 pmm.cCompton wavelength: Ac =-h-(1-cos0) = 1c(1-cos 0)m.cCompton scattering: 1, – 2%3DhcEde Broglie: 1 ==; f =hhnon relativistic particle: K =2m1=-V2mc*KWave function (solutions for bound states): y(x, y, z, 1) = y(x, y,z) eProbability Density (1d): P(x)=w*(x); v*(x)dx=1;(for complex valued wave functionsreplace y (x) with w (x)·w°(x) )Ax:Ap, 2hHeisenberg Uncertainty Principle (3d): Ay Ap, 2hAz-Ap, 2h87'm(U,-E)b =Barrier tunneling: T z e2bL(T must be small)h?Expectation value: (x) = [ xy? (x)dx; (f(x))= [ f(x)y²(x)dxh? d'y(x)Schrödinger Equation (time independent – 1 dimensional):+U(x)w(x) = Ey (x)2m dx?NT Xn'h?Infinite 1-d square well with x from 0 to L : y.(x) = A, sinL; E. =--; A=8 mLE,-E,Photon frequency from an electron changing energy levels: fh(k – k,)° .(k, +k,)*Step potential reflection and transmission: R=R+T =1; k =is the radianhfor non-relativistic particles (like non-relativistic electrons)(angular) wavenumber – and =

a) Given, λ = 8.55 pm = 8.55×10-12 m We need some constant values, Planck's constant h = 6.626…

Answered: 1. X-rays with a wavelength of 2,…

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