instrumental analysis

Please help me with this problem! The example is provided under the problem

Note: Please show all work and explain your choice. Be careful about units!

You are charged with choosing a grating for a spectrometer which will be operated from 8001200nm. You can choose between three gratings with different groove density a) 10000 grooves/cm b) 1,000,000 groves /cm and c) 100 grooves /cm. Based on the fundamental properties of diffraction, which one should you choose? Why? a. (5 pts) You are charged with choosing a grating for the spectrometer above which will be operated from 400-800 nm. You can choose between three gratings with different groove density a) 2000 grooves /mm b) 20,0000 groves /mm and c) 200 grooves /mm. Based on the fundamental properties of diffraction, which one should you choose? Why? A is the best choice based on fundamental properties of diffraction. Diffraction is maximal as the distance between slits/lines approaches the wavelength of light. For B, the grooves are ca. 50nm apart and for C they are ca. 5m, whereas for A they are ca. 500nm - near the wavelength range of interest