2. Given the following configuration of scatterers: x = d. Incident Scattered ✗= 0 20 x=-d a. Derive an expression for the total scattering intensity (I) versus angle 20. b. What are the minimum and maximum values of I? c. If = (f1+2f2)², what are the allowed values of d and 20? d. If I f₁², what are the allowed values of d and 20? Hints: Start with the expression for the total structure factor F(S)=Σƒ,e* =Σƒ‚e²***, You will need the following trigonometric identities to get your final answers cos(x)= e tea exte 2 _ sin(2x) cos(x)sin(x)= 2 3. Calculate a fundamental thermodynamic equation for enthalpy. Start with dH = d(E+ pV) to derive your answer. Use this to give expressions for the temperature and volume of a system at constant entropy and pressure. 6. Given the 3 level photophysical-system with a singlet ground state, singlet excited state and triplet excited state and respective rate constants: A. determine the fluorescence emission rate, F, dependence on the other parameters in a single equation B. Using Mathematica, graph the fluorescence emission rate dependence on the excitation intensity, I (i.e., fluorescence emission rate, F, on the Y-axis and excitation intensity, I, on the X- axis) C. C. Determine the maximal fluorescence emission rate when the excitation intensity approaches infinity (i.e., F=? when I∞) D. Determine the saturation intensity, Is S. n KISC ISC nt t₁ 10 = ~1 ex no So KF