An x-ray diffraction pattern was measured with the table of peaks listed in the table below using x-ray light with a wavelength of 0.1542 nm. If the crystal structure was independently determined to be cubic, (1) index the crystal planes, (2) calculate the lattice parameter, a, and demonstrate which of the possible cubic structures would result in this diffraction pattern.
Peak # | 2 θ | d(Å) | I/I₀
1 | 27.27 | 0.3271 | 100
2 | 31.59 | 0.2833 | 43
3 | 45.28 | 0.2003 | 22
4 | 53.67 | 0.1708 | 16
5 | 56.26 | 0.1635 | 7