In the Bragg's Law, what is the equation 2dsinθ = nλ actually used to find?
It is normally used to determine the wavelength of an x-ray by knowing the crystal lattice spacing and measuring the diffraction angle..
... it can also be used the other way round - i.e. to derive structural parameters from a sample, e.g. distances between electron densities (=d) using a known wavelength (=lamda).
This is used in diffraction experiments (XRD) like in crystallography or in small angle x-ray scattering (SAXS).
And finally, it can be used to calculate the angle(s), for a given structure and wavelength. So you can design an x-ray monochromator, for example.
Bragg diffraction is used to determine the mass of the pi- meson by measuring the atomic transition x-ray energies in pionic atoms (See http://pdg.lbl.gov/2011/listings/rpp2011-list-pi-plus-minus.pdf).
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