Question
Please Help
You are designing a diffraction grating for use in a spectrometer to analyze the emission spectrum from a gas. The visible light emitted by the gas has the following wavelengths: 447.1 nm, 471.3 nm, 492.2 nm, 501.6 nm, 587.6 nm, 667.8 nm, and 706.3 nm. To design a diffraction grating that would allow only 1 complete spectrum to be observable (where all colors are observed), what is the maximum allowable line separation? (It is possible that a partial spectrum is observed, but only one complete spectrum should be observable.) How many rulings (slits) per mm should the grating in part (i) have? To design a diffraction grating that would allow only 1 complete spectrum (and no portions of any higher order spectra) to be observable, what is the maximum allowable line separation? How many ruling (slits) per mm should the grating in part (iii) have? A set of atomic planes in a crystal are separated by a distance of 0.313 nm. Find the smallest four angles (greater than zero) that an X-ray beam would need to make with these atomic planes in order to be diffracted constructively by them, if the X-ray wavelength is 1.54 A. Find the largest wavelength that you could use and still observe at least the m = 1 maximum for the same atomic planes in part (i). (This helps show why we need to use a wavelength that is similar to the atomic spacing.)
Explanation / Answer
dsin(theta) = n (lamda)
theta = 90
d = n ( lamda)
dmax = 1* 706.3*10^-9
dmax = 706.3*10^-9
b)
1/d = 1415829 (m^-1)
1/d = 1415.8 (mm^-1)