This question concerns the Compton formula (Eq. 3.4), which gives the energy Eout of a scattered photon as a function of the energy Ein of the incoming photon and the angle of scatter @: Ein Eout = 1+ 4 mec2 (1 - cos(0)] Where me is the rest mass of the electron, and c the speed of light in a vacuum. a. Write a Python function that takes an incoming energy Ein (in keV) and an angle 0 (in degrees) and returns the scattered energy Eout (in keV). Your function should be preceded by comment lines explaining its purpose and use, and detailing the input parameters and returned value. You should also include explanatory comments within the function where appropriate. Test your function before using it in part b). Considerations: . Give your function and any variables meaningful names. Remember to import any packages that your function might need Remember that the Python cos() function takes an argument in radians. The mass energy of the electron mec expressed in electronvolts is: 511.0 keV Paste a copy of your function, including any comments and import statements (either as text or as a screenshot) into your answer. Explain how you have tested your function. (4 Marks) b. Write a Python program using your function from part a) to plot the ratio of the scattered energy to input energy, Pout for angles from zero to 150 degrees. Plot three lines on the same graph, showing the variation in scattered energy for the following three input energies 17.4 keV, 174 ke V, and 348 keV. Label and annotate your plot appropriately. Your program should export the plot as a .png file. Paste a copy of this plot into your answer. You do not need to include any other parts of the program or notebook (4 Marks)